Best Known (83, 83+∞, s)-Nets in Base 27
(83, 83+∞, 324)-Net over F27 — Constructive and digital
Digital (83, m, 324)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (83, 323)-sequence over F27, using
- t-expansion [i] based on digital (72, 323)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
- F4 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
- t-expansion [i] based on digital (72, 323)-sequence over F27, using
(83, 83+∞, 325)-Net over F27 — Digital
Digital (83, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (83, 324)-sequence over F27, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 48 and N(F) ≥ 325, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
(83, 83+∞, 2218)-Net in Base 27 — Upper bound on s
There is no (83, m, 2219)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (83, 4435, 2219)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(274435, 2219, S27, 2, 4352), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1884 746848 057191 538113 239807 516490 883584 996356 732804 990796 659387 953131 666323 265785 812359 241661 997964 781938 016746 099875 383695 478597 106632 094095 444739 176308 608315 965549 403975 807271 792795 420160 222921 059337 676668 798051 850601 619732 717057 629491 352476 744108 342416 270239 736642 181888 538410 023239 699061 908852 087527 460075 534633 615637 343116 821793 509454 621402 474839 218028 064656 361820 033083 782667 650597 334073 875606 986096 028460 713456 702433 247030 540069 055620 537707 301742 415814 279345 424561 497238 359644 844024 067787 247580 657630 142508 420719 000175 314924 448219 859395 228100 051822 275079 505465 896848 000764 810250 532889 387844 384709 711083 884717 474112 481293 066533 088568 142176 716478 127408 046610 580572 813612 954186 944200 309068 795450 710408 719869 011489 568241 171727 450517 312320 744963 173964 398685 293182 145107 271903 821336 529349 328729 197788 049867 956190 475670 566814 706605 026196 242676 821917 094118 165045 670586 009315 004441 281241 654431 733406 679736 918139 303978 629799 650885 296031 958001 823657 662567 039759 120686 510670 488199 869697 920750 714334 935787 963115 999145 317346 434034 433250 227053 598252 580306 863552 459701 201881 561603 631045 591781 980301 765547 351162 771447 271317 788958 893880 454472 068680 020344 761242 450339 310486 033628 437773 390220 211062 076572 995602 190907 576189 853977 387363 739737 547578 095141 645269 577925 185665 602892 326732 419418 010287 397297 220441 409117 164817 293281 167413 760651 805456 610104 487712 990859 324790 567659 311744 998350 981922 850666 764107 768706 898107 689926 492578 098065 176360 812242 490235 345278 885838 554593 419117 515429 708261 238089 990529 400669 136095 920531 892192 753504 553901 457662 614774 244928 603139 012530 000446 140250 392878 607956 417644 183143 248647 885332 998169 402141 513098 372565 791701 379056 390946 716848 828578 968624 628367 455067 365055 017451 936831 112387 881997 501703 460914 240979 941336 903175 455631 821486 903177 331876 910418 419693 288919 039717 758271 167893 165395 405473 595238 582442 897096 356924 458062 243691 642728 243924 151690 313325 068219 957031 672660 065906 212928 559679 696038 646847 151819 745897 907367 799620 037161 376844 376374 309363 547411 465113 652519 262824 337217 499353 444031 840421 694576 544911 599686 129745 949892 200559 493637 125421 776795 483710 061376 717292 074575 575951 177369 913115 883865 721816 788115 635651 419920 814269 091366 958182 381395 751938 546225 911931 017860 798774 944515 216901 869503 874944 905525 630620 398575 705100 637197 789130 148804 142424 394760 172811 299573 430864 848629 293578 861326 523473 803752 670115 798550 273806 513969 293614 685542 472443 850011 579957 856130 061119 825221 050959 853592 763957 012265 599181 298312 805332 491973 171046 982932 825032 401408 973312 863584 607505 157270 103330 674258 410750 911611 045879 614688 070679 332321 581860 323862 348956 267941 863040 481767 673237 586979 240093 410104 786499 347969 397668 317166 886272 826617 215889 604291 446313 644679 172870 564477 049849 051665 337274 272580 488156 504410 498202 305335 172897 991035 209571 039400 280860 773756 477427 081027 412335 600239 097435 487763 140837 787321 316217 109816 229146 194734 346885 133553 238325 437273 626715 961463 135988 704283 524566 753532 087777 824795 280544 531287 536731 583552 154658 672055 305906 998272 766330 031707 959319 818308 685075 388733 968656 451169 417601 720015 927286 963239 725485 995087 503781 983520 898872 103268 075479 208660 442461 502367 970663 933240 925228 993404 589313 147788 477656 834012 964490 859242 153693 609563 945381 707769 401622 920358 641072 021565 263858 455566 686781 307738 044419 104643 546571 102919 852235 392363 011165 792996 920352 227488 794801 076759 474408 960374 880368 518726 214802 942150 761960 123129 941046 596888 109500 142474 844941 816860 723342 526172 724579 401808 085096 452246 871383 819185 803910 364404 392398 321954 890023 983500 331298 853144 985170 388163 986570 559939 698989 551458 678581 337442 618740 520247 773082 718726 796934 703018 978859 734412 159788 563448 229295 567215 679410 414099 655959 017879 569796 271809 097058 640201 642341 653870 165367 660417 731208 892119 560306 036013 590504 216490 639613 093955 798530 718283 841033 002394 143893 212502 939434 541432 647374 780986 604731 974888 277872 105654 486528 983803 418805 656192 080373 348701 514788 156035 159656 773886 976674 880397 608992 911488 795113 143444 924088 632896 915288 681554 645222 692087 148492 039461 172560 409023 056450 879029 442468 175176 260279 829487 160505 901324 764658 999324 930024 878929 651082 717613 066586 236641 479323 534559 283837 144632 877474 990401 322056 524237 082786 441370 088652 447078 611463 238775 063405 099949 917641 469186 123464 893588 968410 510089 541697 047682 044986 387479 951460 433058 995905 892895 132928 014853 487671 884295 814427 603574 569161 875815 025893 866566 207948 258166 222778 151393 571789 309367 491752 631292 165015 480808 081183 305080 246297 564738 985334 806857 674412 554023 171284 245840 984068 661309 389845 339649 286152 682379 295659 544039 407946 387271 527439 100773 213311 593470 086518 446529 077314 836555 185815 881853 712687 749277 785021 031304 073862 022652 316124 955267 442346 813645 604584 606117 024548 473099 842116 641185 764655 599079 900299 340478 932776 031000 206841 555453 256650 042374 225207 291196 079940 309921 315982 429070 176089 157661 589731 665485 600397 540965 619494 488198 488383 182853 035424 188659 464256 072341 011402 942910 173930 750654 004746 167931 474920 822528 682582 973893 248457 227129 176045 898119 395359 487842 766423 282548 218363 923497 015525 931270 036167 012433 665867 246410 277892 317029 318212 624178 203355 484996 967217 008390 682287 931319 484799 423146 793653 623881 207296 036956 916253 508276 462549 758490 386670 364848 857809 060645 333464 931045 489679 917714 913777 243114 078974 340782 091655 175633 641323 321235 943462 887243 087523 881511 068556 043183 757924 101324 627020 830834 533873 217588 222930 026744 887064 682285 379626 433974 215506 182494 294214 995740 977928 373018 552905 763466 953200 276281 446081 498807 278543 156309 743857 174041 769296 717661 871716 679766 241408 702892 459235 912781 512781 861744 218502 635240 591960 860303 603160 122371 495265 694042 794434 946001 673130 685892 325531 584092 648381 523006 147906 354440 554558 657319 741563 077372 446451 139899 751626 735215 473769 794636 454943 020783 728139 011333 459072 913751 065392 048564 124983 909526 190590 342690 420599 368582 110027 224981 439568 919879 994556 845751 095904 539976 175212 347883 974564 663685 727086 988134 352769 258963 933888 144939 386835 176350 001637 071453 347902 057374 857200 791859 969083 357539 089657 572917 768452 859767 957537 836549 939833 918780 120049 152720 774293 360983 712413 182651 050150 510515 259071 185773 024983 076169 772547 269097 321294 566853 274251 174873 855423 078621 560603 256670 445879 360276 640824 946708 700572 652824 955230 018060 144178 896720 870757 373978 328602 223341 878917 409850 887666 790098 115731 571288 369031 466315 080716 765612 673831 191450 435915 517536 985511 599471 798440 583266 006555 250281 411771 609162 586838 703832 202529 985810 324671 334031 442310 385821 920194 885526 527181 470588 283129 994864 688457 604463 362070 854695 919229 / 1451 > 274435 [i]
- extracting embedded OOA [i] would yield OOA(274435, 2219, S27, 2, 4352), but