Best Known (10, ∞, s)-Nets in Base 256
(10, ∞, 267)-Net over F256 — Constructive and digital
Digital (10, m, 267)-net over F256 for arbitrarily large m, using
- net from sequence [i] based on digital (10, 266)-sequence over F256, using
(10, ∞, 513)-Net over F256 — Digital
Digital (10, m, 513)-net over F256 for arbitrarily large m, using
- net from sequence [i] based on digital (10, 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
(10, ∞, 2827)-Net in Base 256 — Upper bound on s
There is no (10, m, 2828)-net in base 256 for arbitrarily large m, because
- m-reduction [i] would yield (10, 2826, 2828)-net in base 256, but
- extracting embedded OOA [i] would yield OA(2562826, 2828, S256, 2816), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 49709 789939 279070 930692 155468 160982 668557 388029 028979 538335 524139 376724 310091 214115 131377 593436 551057 596090 190366 470924 377911 089995 752097 066009 799712 845088 529340 913123 565334 132144 143596 523245 354882 135375 544488 251745 167017 943737 419272 706555 944736 206598 646690 669976 224073 654272 160388 595464 521870 626072 424946 630422 915371 637040 895890 731726 435904 388229 077226 042061 272857 418332 469834 485496 823638 987191 323391 098203 243070 012863 919468 324243 916956 785529 034405 169046 349443 551156 945180 620877 721684 717376 770592 750040 692637 454708 224550 416391 988714 885267 550853 388417 514014 922379 373399 498992 372029 626013 229458 491362 745965 994030 523525 187530 313500 147122 164867 537737 041160 424309 870003 295225 595247 829122 209731 854630 068236 115591 445049 986174 818100 371951 389689 409595 590183 307873 645820 440049 776708 906792 339955 865702 193708 815813 142076 384452 701925 668715 995931 966477 412994 935408 767276 436249 977190 100449 112197 062192 084107 859909 179378 423918 668428 408397 959168 641211 488845 047210 951947 343417 529991 863351 697176 428326 377622 785820 399576 305870 523073 921929 750082 443486 509588 124572 994228 786420 533744 505149 751895 684041 416907 880687 736105 416647 964904 882736 040439 414890 746131 429623 013247 620666 070590 042462 005143 452734 225716 140951 752696 223299 246564 949769 902731 874754 039070 200522 009629 815042 430893 414747 621682 099446 765389 187567 787664 398877 169585 132603 527223 925691 413585 313006 851475 965197 574212 601924 940984 395534 880794 817437 898967 713299 368152 571330 933245 726441 183126 265399 849585 759987 418526 133090 550531 504701 536868 348771 269303 527419 923079 560802 782120 613947 411325 153234 476500 028093 795623 726497 113210 664692 178050 208150 837238 665574 715651 956485 400531 903291 967534 842068 250562 750517 566214 146257 202439 893489 496202 560599 402668 721999 058175 169687 677811 084874 619102 016200 710056 038956 845097 508959 000454 770166 848090 302679 579220 270126 058585 243583 414433 593556 316046 694604 372537 703416 531614 448448 417387 687927 350177 436368 874180 002183 491527 085121 344004 760518 081483 481976 101401 330443 464236 304499 082636 759368 676124 664506 567211 346517 416749 499990 358704 403846 694967 375481 687810 601891 120294 022297 366122 281414 290310 847486 061388 479387 462380 146399 627695 045196 144824 916890 285335 293744 362217 046030 717782 135394 112504 209200 822379 144670 533431 502450 194013 728540 827232 734327 846918 144954 968371 823650 720321 632499 895671 839895 470114 229893 799840 547318 224908 606932 245100 603769 717368 415487 081836 395795 908557 480065 346280 458760 373265 793858 866844 158290 330504 442395 093331 384635 415153 735250 012287 878896 550107 707403 021322 681087 320810 529080 585754 508803 457557 216699 412180 684440 663721 096166 645390 435271 176172 495907 284073 540932 850544 289961 250869 788155 755628 210555 181845 827422 521573 360464 647208 344918 928867 830591 240797 897511 415337 203576 192185 977964 592061 094988 789097 189987 807504 144072 208723 607605 522366 203440 944390 822149 653028 385299 122466 784688 224406 938273 363629 637012 653630 006062 497044 781747 039191 318545 565849 461807 240102 453711 491699 922606 356011 363147 939377 894598 287342 149042 040833 599854 061282 600798 995084 226355 750292 054051 704255 921745 598341 859312 801427 575820 505678 431386 731562 099365 097794 941953 857748 037398 077866 405160 254465 455021 884577 692188 615215 671041 548126 489296 486280 366019 379749 210691 967576 108169 215386 132882 207389 078511 401134 247705 424259 970327 131425 221507 128598 030527 870580 636560 273980 160758 697873 907192 537184 417968 030649 007151 514887 096967 361848 246985 693009 021693 363665 705132 972059 320887 079265 990784 126533 728894 324320 021839 687944 289775 513006 827289 941230 464285 715681 379425 249081 841287 943588 459299 101408 347544 347597 297132 436726 986778 231722 094695 691616 344998 348506 566765 605718 580926 253991 558147 681427 875159 701784 426407 955602 525625 467586 005222 488032 690114 757312 272036 823426 325690 279619 985921 070280 230427 468771 092288 537028 650727 797831 839551 957410 502233 771780 511115 619255 912400 657153 476276 661246 875478 876705 027711 047354 188206 273334 017832 454078 389686 612863 154034 725129 458413 554390 518019 119548 475140 264149 663336 727004 340882 079437 488834 832279 600918 438081 571642 496016 870630 346202 995681 311533 859967 998762 470787 165946 555088 371826 698317 243331 323782 545705 925000 813046 593308 071826 132161 003614 936757 698983 521141 478676 636585 387865 274219 118943 265554 730592 386744 333581 527615 122815 040594 595441 687581 689454 436209 698788 740324 936623 377426 173591 894879 182794 964543 558070 086375 409690 250049 538348 958628 099581 285649 792326 575746 461756 473342 272525 329961 529803 310326 807148 815599 003223 982545 148984 863240 996849 626503 715429 471828 785904 221786 097439 777163 605346 540895 776447 924352 298367 510227 554702 979822 141091 110657 456513 472825 424761 895974 421698 023182 015348 770504 018539 230621 825576 029477 667156 065955 578552 494010 115635 964096 460033 258942 256843 663716 968928 888087 569988 333391 475756 726742 246509 349652 625469 457426 088728 692920 026148 419309 957559 834830 443516 817138 906829 597349 466169 919977 475250 104921 992295 108566 338419 406113 931425 989939 211574 491856 232446 725183 011590 847154 299754 763509 086507 008806 547133 608167 260998 388218 805801 032346 508990 855983 832865 555355 364761 249711 443806 930199 193041 461758 712470 942800 739778 725723 423424 518169 048126 377940 912420 074804 733746 642704 350821 217276 776645 464488 994610 693619 305612 857016 616992 308911 678814 251934 968106 019901 348755 802475 394184 993425 995032 405789 614655 555979 488402 754229 063346 820552 065246 516140 372358 931081 560572 752709 986941 224617 330479 464545 791501 039174 256461 089076 999317 054342 508344 449665 215373 509035 659272 139723 505482 771354 524031 493461 803543 767095 038183 094036 711785 759517 795183 624011 181672 789630 431807 491372 795560 943936 304775 531865 668700 502765 829435 394842 506337 997396 049428 141550 283721 737324 438856 513977 074089 809637 649477 317058 818415 944776 575483 056588 304113 163547 193875 837435 534819 547317 025342 838867 315362 902375 033711 256791 272451 902463 668087 969001 947045 053668 044817 186444 432063 324164 443193 311369 813685 503178 982937 045386 361363 451855 810651 312829 273055 081828 859201 195568 054270 749825 963585 730336 635367 931757 453304 872733 244040 792325 892028 659610 947292 418198 385212 422185 216262 003185 247153 278371 476182 569561 475441 123970 440970 273725 558088 154913 039468 609248 368014 512459 360762 571768 231986 947508 329425 158997 809569 369004 652333 066431 483864 675519 161876 541564 283564 776811 594435 719624 582739 548297 179344 972399 818815 000834 208231 584079 940385 024649 348074 220478 585941 033203 344319 016748 180151 185406 788904 532633 329736 515691 807698 066972 526904 127518 792003 039436 376090 428549 908350 820161 851267 456655 673516 008848 547848 883752 756757 517164 099002 002648 091575 766034 334960 337374 021833 411227 436508 547695 197414 895315 897405 302525 896183 177368 575956 545092 604516 700251 936803 128063 159830 211921 890268 292906 604390 537732 135100 825171 162251 310441 596713 042483 711038 570819 413555 462740 292401 797040 056390 442919 682891 541901 454031 058886 780415 205144 121454 080043 491474 124861 289235 793181 009279 793854 423959 986053 017456 781573 545821 825991 454891 803793 430187 252679 893934 684075 782883 356574 592445 320204 408656 938597 424098 729375 565708 050754 360447 443376 504952 825278 577664 728356 586839 943353 502443 533313 688122 312280 759932 938242 483130 439290 075970 806748 851634 124980 486144 / 939 > 2562826 [i]
- extracting embedded OOA [i] would yield OA(2562826, 2828, S256, 2816), but