Best Known (14, ∞, s)-Nets in Base 256
(14, ∞, 271)-Net over F256 — Constructive and digital
Digital (14, m, 271)-net over F256 for arbitrarily large m, using
- net from sequence [i] based on digital (14, 270)-sequence over F256, using
(14, ∞, 513)-Net over F256 — Digital
Digital (14, m, 513)-net over F256 for arbitrarily large m, using
- net from sequence [i] based on digital (14, 512)-sequence over F256, using
- t-expansion [i] based on digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- t-expansion [i] based on digital (8, 512)-sequence over F256, using
(14, ∞, 3855)-Net in Base 256 — Upper bound on s
There is no (14, m, 3856)-net in base 256 for arbitrarily large m, because
- m-reduction [i] would yield (14, 3854, 3856)-net in base 256, but
- extracting embedded OOA [i] would yield OA(2563854, 3856, S256, 3840), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 931 507293 840705 726420 410637 940806 242235 236403 634054 807059 607281 560748 149913 736700 329909 748488 371096 435053 183813 702193 872309 797484 404254 499315 170880 200994 033228 321319 593373 493194 360594 819312 248905 164325 728045 255372 672002 656726 826866 301847 707440 818370 159508 739122 597020 950455 366285 690632 429149 173433 153604 696607 248841 423561 610246 821132 609127 816610 698306 636029 088863 934516 531060 154529 706394 198075 209238 426213 768237 628470 696020 776469 881171 312829 862532 307467 493479 869138 460147 069025 181199 380063 579187 994051 344048 014259 865188 068114 332108 778665 361496 577940 379751 485538 504911 785454 847753 731555 836828 018426 692478 082225 585553 220325 146847 757813 873165 388637 964772 013047 025749 463724 209103 555543 677890 048273 457364 638746 744904 556572 958428 428980 023127 375469 959116 086944 460513 283527 398871 354846 914432 144777 174919 176674 201584 173336 104817 643446 455389 797720 983072 991531 715784 499647 126635 829532 969908 700060 638803 934681 887495 135943 432250 840687 983921 569588 083375 524414 431629 450141 766996 076855 242082 684256 595030 811922 529048 883382 976434 613778 846910 982376 600178 060563 631271 526432 756439 263880 700612 851273 240119 985109 047465 949631 346146 519925 059077 517900 930331 572070 277139 664548 876858 306254 441015 405387 503060 676361 749097 515284 656977 183162 742246 157262 853698 942252 331821 469631 838146 774446 554693 751758 054604 526489 191245 929275 716509 031279 890533 188235 668689 960266 719039 394577 743148 742955 931106 795578 787849 317902 880668 026128 299481 903804 678536 752800 284710 406967 390337 512967 218900 197715 673579 235738 356564 837152 353467 103821 270157 773226 999723 232174 605681 406750 809066 494956 947614 608536 231252 226574 676257 607204 580549 702831 675566 803762 817858 624883 446796 712095 599179 037170 039619 531264 163404 734322 753227 686378 773052 494347 100673 768059 750917 684404 123474 352160 924875 618504 382512 023219 689348 286252 705341 628339 087596 728239 277033 273455 303527 564817 606535 344346 699916 182523 324374 607995 408848 080922 531249 328409 898870 058963 991362 271122 208365 069418 031950 341358 809427 960770 911238 713470 820525 098447 768643 768377 040088 101501 677594 774391 858885 147205 756079 253235 544905 812685 224423 757866 136807 869256 393651 504417 929732 006166 747029 479588 972958 319656 421127 572369 799740 935338 970454 696880 248976 359448 398736 767536 438106 961681 254458 938011 588876 134402 168894 898834 936799 467535 469299 718217 061124 257979 048999 538522 382109 289503 531119 884543 658609 808237 809679 493063 354367 580974 848129 950126 189630 518621 866199 579924 536446 493536 613657 842636 353656 799232 482549 349797 901133 197423 317413 702483 419378 889366 126529 262854 911997 550690 563694 479514 434746 269716 500648 334083 102274 640298 473962 806594 214438 626406 878348 898146 540356 676196 773818 169699 356711 062002 823844 920075 504751 429654 566047 024279 767016 324158 737477 957274 283039 373139 129682 579140 175501 337153 774713 882663 897957 125663 006884 277381 240802 318637 323059 023216 305995 717462 205194 320132 703414 572910 780005 346818 517710 348994 447574 847807 711771 200561 812078 432328 447022 419531 046582 867630 781044 417324 755792 891365 449025 327894 222197 200280 006524 614377 331638 339725 830225 287488 703318 159681 327089 313019 472339 926982 464032 516116 070914 583707 570473 420947 456620 350339 726309 448721 346786 405057 349766 621275 573421 884121 835492 273803 962592 568790 222964 870052 965673 907881 688662 502367 618914 264368 920127 687985 375182 861460 025124 609592 795063 344387 933773 843686 471531 036672 206222 992376 097475 387909 888583 565461 917267 945116 020066 172814 921856 034075 046384 282954 535130 229737 063045 853989 665072 835800 007690 250604 067480 407321 691320 965819 914876 069763 776777 367334 902989 359597 885600 677127 177367 241778 369231 521500 554573 683052 597409 630272 680448 742455 294546 805197 355689 582132 955793 541452 023671 974724 691739 632501 436430 047150 888394 942312 721158 973391 616883 656921 420846 706249 798613 366215 618279 144490 852898 597244 015349 682604 011859 405959 524877 145364 256079 878921 440560 600318 291049 285551 959849 987884 246981 643422 199847 577038 462302 842189 454208 200937 186785 540662 417175 889350 791078 866692 284419 362829 301250 637944 622484 165108 272865 933282 810147 477930 976159 506906 677044 100403 896163 130863 079775 520649 080236 456528 406248 038576 626704 245690 583019 680177 892982 195556 477013 300467 043973 009114 182371 721979 295091 403838 996940 482571 760902 766267 251909 267057 458502 391926 599898 088899 433463 623897 798447 348955 929518 963449 477133 832764 767689 029682 420944 983263 599342 226834 010293 185845 723150 804565 226506 689303 850321 858495 844688 605740 474433 381669 574460 963742 442141 602781 914479 053086 176238 100058 379878 915001 970834 904442 201197 026072 934638 928865 865568 311174 065785 311155 012452 955890 245893 187035 393709 651068 236797 472553 739588 617407 727542 151671 020633 186415 498532 239349 515997 527181 246950 109428 150084 497828 731228 130033 886300 370919 655445 167518 338468 962298 291076 656077 372996 280034 612367 486595 288067 566552 185284 441713 238844 357871 113406 516903 236243 469664 629246 558214 149901 059369 264265 325779 046395 278060 078193 750195 442920 341033 020877 321460 036281 903189 376985 163898 871127 505722 274222 292151 182448 935266 298458 842820 380001 760470 074355 755532 840652 710161 935566 619475 403605 344585 180993 492960 276458 794250 846187 963537 086912 022586 654872 077925 719884 733675 374721 741799 917698 252608 859649 606265 521693 953627 391410 190430 328751 391022 007786 726593 157241 424494 120392 677513 657135 275621 374807 344747 044753 503867 514858 699999 048241 075977 038847 748126 535036 592852 597479 810329 690926 869539 092847 940308 193008 113163 692078 384077 536765 351426 362429 236678 403324 791333 528914 912568 543686 204335 263212 106238 657200 551873 556051 458740 642135 173915 790456 724362 200139 055701 660974 324215 852360 061432 783208 187969 707481 527642 583064 119243 734659 821894 327003 162529 002064 588210 260637 944432 106234 840988 021749 020984 492613 768966 048744 010214 029148 183836 228605 346361 676108 023310 883966 525316 390964 159024 978709 538774 533728 475503 540243 575116 935619 577708 477596 687316 084193 979779 677243 254875 534032 686032 299370 235212 388434 945502 920243 304278 151427 701505 946426 890932 370678 248061 964088 249718 957367 085631 779955 933862 365529 728364 154301 494205 163012 023050 377562 683798 998892 551572 799876 381856 116712 346421 484437 716866 614240 682446 850337 873805 585753 940559 608137 814133 073560 857774 647026 305427 126584 673323 306012 275718 746526 229852 366781 289392 573122 917186 971875 393211 930446 186286 692587 441265 918096 629293 124656 415450 129592 753373 950173 099417 593070 030749 219367 666017 392875 303469 699043 990165 577202 524569 307506 302329 174593 825774 931356 139444 764233 214586 223488 066555 304560 207657 337558 778255 667385 190883 453257 380135 372754 407844 297094 703420 183092 629123 149417 425826 452417 471926 085869 668911 133684 159812 482932 018096 554511 382379 057441 165696 791838 098789 691086 248394 548154 671077 637670 830530 570769 759375 889473 654429 370325 412033 412846 534008 326674 132473 725349 997851 488691 418456 398120 291294 498048 038222 124075 022566 748461 322059 144798 363913 556176 895022 757667 618639 911746 731340 608973 669160 910706 483803 401996 103091 373145 213415 703906 373372 258529 613592 073342 750003 176571 342339 220778 478455 879850 762364 427382 326370 898100 520289 041118 709765 759181 714254 834305 968723 227885 438532 753057 564060 255147 209453 319127 655509 547518 207519 006286 589818 391892 968793 434033 328982 615057 691757 573029 802734 926669 961591 716140 300906 763041 442461 192545 472821 972794 484317 934099 068605 792304 283186 987604 717054 994038 616196 304515 718728 071556 212916 211832 536549 743718 934856 996265 682461 047229 030657 702348 785480 775178 474548 985498 771877 357548 302707 913072 356894 489976 254217 734145 273667 254053 801614 384837 827933 099742 279119 328376 308093 288036 935169 379454 392609 856096 880007 183083 326600 767048 242404 977165 824331 618644 296438 487163 262570 394272 840933 306376 506000 378071 566080 559727 465236 924912 137517 675703 478516 052774 840940 337960 537586 992470 750855 575639 280720 445785 786249 970894 383623 467380 818145 083219 761871 969686 590740 835943 938521 850833 996027 848625 739554 876952 297420 083283 559923 458526 123695 059435 423802 368648 872091 932100 975799 899058 937342 682368 552682 660178 252027 886919 890949 099594 980559 826246 017822 023459 545942 735306 062861 796307 993396 072740 034676 231521 928244 974355 559007 814592 240076 013414 205367 924919 374005 477228 892700 433078 471689 595575 340648 108977 612293 190633 225763 627058 901390 269846 848095 312954 696077 830179 278548 423412 782425 150572 608727 055908 440182 248870 367392 655005 359084 679202 689741 431651 721310 232421 401134 712670 109349 036887 505871 018275 456262 887404 718647 517616 871898 469027 726368 917464 356845 634876 916135 690576 139931 827924 577265 085176 822438 146268 565491 957346 109248 048770 051050 441835 936493 560523 882388 290364 742086 995023 314814 042870 533272 411434 819785 337269 880335 263546 876035 273705 916711 598277 380894 810352 102906 296458 319632 363499 815515 693501 555212 576269 894145 155656 875882 170295 327699 134010 967566 905067 534866 783788 163899 416702 020551 287152 775345 362528 656560 019904 913944 610518 004988 927759 494339 093994 952352 958778 898403 309001 356137 682324 323963 694957 201510 029978 165002 671242 146734 839897 368001 178505 022341 370210 891702 763599 563389 314346 157514 232579 634143 025746 648858 360903 910408 194202 203795 170690 857329 732808 325765 604221 621093 686807 860031 178375 744769 117729 567211 591767 767407 996999 616485 587663 160571 823555 149341 090714 955214 066996 942643 265115 168435 895953 245510 632122 860993 892340 096624 030546 428467 970494 727066 215592 379967 422355 529034 474470 054103 944230 631163 143174 343260 469256 515890 568283 684891 521259 191064 568659 758284 575226 420758 112464 227890 771792 259012 851937 897557 129254 537022 176300 704567 615358 965066 940810 309533 732077 442993 976429 530702 127992 621332 553743 620772 989631 181347 595130 182315 907393 769369 905309 559643 396486 081521 144824 351122 780965 566598 498793 602140 050914 116843 612993 435262 170927 409662 606119 675213 814861 695984 300491 199701 148575 581730 682467 104699 802589 379408 970909 638989 410694 332416 / 3841 > 2563854 [i]
- extracting embedded OOA [i] would yield OA(2563854, 3856, S256, 3840), but