Best Known (35, 35+∞, s)-Nets in Base 81
(35, 35+∞, 370)-Net over F81 — Constructive and digital
Digital (35, m, 370)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (35, 369)-sequence over F81, using
- t-expansion [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- t-expansion [i] based on digital (16, 369)-sequence over F81, using
(35, 35+∞, 612)-Net over F81 — Digital
Digital (35, m, 612)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (35, 611)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 35 and N(F) ≥ 612, using
(35, 35+∞, 2952)-Net in Base 81 — Upper bound on s
There is no (35, m, 2953)-net in base 81 for arbitrarily large m, because
- m-reduction [i] would yield (35, 2951, 2953)-net in base 81, but
- extracting embedded OOA [i] would yield OA(812951, 2953, S81, 2916), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 26 060182 564839 302143 176642 101087 427392 857316 829048 830417 379363 669192 516218 313200 696112 533030 057583 245540 589845 081727 765141 211967 632055 303448 291018 765925 089101 008470 989984 754136 520892 490090 549628 164804 684184 755882 910868 460176 491128 497622 100020 893256 265284 125002 382787 893903 846163 100640 660595 656533 563374 600570 793189 525901 041448 431549 380386 418992 196601 081516 334901 922266 781519 377020 652453 079582 843738 122545 613546 712449 741701 124548 585746 047399 988576 311107 296297 765164 669776 974165 831641 203338 219059 901780 693853 124027 669163 040172 101792 260748 188060 392616 979872 995893 213122 132327 639431 895109 788197 273086 136538 352839 817335 005978 426429 094780 963280 819670 164689 598200 904307 432114 745575 193809 232074 395577 422835 783206 819315 720275 595198 184182 631625 287500 900169 641436 146543 784335 601360 150324 148615 181472 541278 254893 569809 085724 981446 043625 686228 287712 655598 628925 402072 247306 418013 195874 384498 627145 158995 434964 623524 127158 665637 255366 656366 944079 664343 609289 263277 050593 455391 803852 119330 185509 517842 522903 848516 595698 366121 122005 692258 419507 358646 652127 123906 044462 382137 130867 512133 362221 720261 147998 666403 697448 095039 987639 070687 432034 188271 799323 047979 462665 779254 863899 362073 515691 068990 548563 011812 469196 292423 737427 484820 068853 579271 037885 522914 272201 470407 946236 447867 194292 989615 403611 687952 853055 629397 878224 824982 667951 947602 843283 372128 083043 140443 479927 413165 547578 220956 330303 850561 829430 412384 950235 756184 308604 393556 349613 371881 500409 764529 265432 253193 265665 810685 703594 976312 588871 425171 920387 969339 679171 092133 564017 674550 027992 148575 306844 554139 667160 455855 101218 146399 985725 834606 722263 414113 086045 867763 911794 228038 206659 062896 343379 727356 966672 830592 336042 432934 866167 967972 920371 131689 461469 336272 413348 093286 846276 573092 526609 841701 539041 481531 756234 800154 143987 097787 569666 097577 781474 170555 722025 056602 478649 716124 693583 212596 575303 539553 136195 076502 955212 985849 309298 984472 486613 358516 932567 006553 917489 937679 433885 537741 092343 756767 576295 294410 976569 866793 539280 208829 920884 130873 110721 847904 021267 611021 845406 134511 624752 207343 414601 645795 717636 839894 430807 205325 045885 602638 521334 576148 965450 258873 301552 694385 726376 287366 115128 335557 279422 069409 886407 582929 089732 263376 932053 559019 743703 300874 139868 738753 185226 139828 261299 948224 005698 146281 819977 427970 658663 909145 942783 366955 239586 134515 400371 441930 413781 002651 930879 643976 449642 869889 310069 908357 859512 937777 440662 399518 462044 612370 936570 397210 942012 949515 608835 148270 741855 312712 371782 674302 781669 361663 569830 701173 185401 537286 900754 615782 586650 287167 404701 486067 837755 679717 321912 288191 835292 220696 604254 722513 099242 689617 658659 151211 666295 496378 814078 760266 058185 284327 525353 278035 804580 943750 817312 768511 199841 907567 758051 537386 924969 175480 086324 278137 161035 563875 019522 054922 576617 039767 789469 330083 466408 247453 361215 912644 002753 352997 743918 237591 706453 019134 657397 382487 411458 440726 611867 201603 466615 611926 315776 364233 808378 768593 116684 275262 515092 772851 665381 145093 206777 327052 483571 432127 690513 573872 974451 907924 976562 509420 404323 756626 076399 557367 091918 343440 976990 109821 194314 332040 120722 975785 328028 072971 049609 234101 523241 895752 120339 418114 962491 343697 864847 266512 846564 098939 149438 494136 749769 093605 852240 991587 010599 159379 821332 321121 652479 344438 891396 518367 559348 717915 319402 028807 048682 317379 404738 684129 312691 400769 350915 246708 265188 140897 097586 253433 421759 341896 378537 999311 476466 462093 916459 206135 304783 508437 012992 076093 188957 072608 722693 246583 221794 115305 371138 466150 740883 517301 306662 447883 003062 817680 724926 720421 245704 537441 664999 475373 276018 781944 669599 016124 428478 506322 233447 558296 936674 690704 070089 034214 293164 623035 001880 057141 735500 875528 277737 330276 219465 167404 500676 206645 725609 084690 446025 389124 581312 604091 415944 589890 284724 114110 995702 802917 803863 025762 758240 530603 268631 918352 533632 988505 486577 274485 714619 032835 105709 667312 016300 444355 897618 209283 427146 230487 777755 731965 282784 908122 548670 194541 872436 185712 779399 925488 884556 833781 081837 400955 632595 615028 452198 863515 669102 136973 465050 178790 382788 121122 985003 081620 750863 098722 912717 443810 918372 805252 624007 279145 139443 737523 920488 188850 097765 052812 487713 294037 650460 471988 593434 564180 823178 480134 823062 336539 554432 534876 220399 631136 956401 545958 392328 993644 030716 611561 437957 859451 069071 807353 158907 526048 649708 149013 587478 979599 229003 763433 300564 193721 357278 134427 994560 294458 718617 392022 635646 595944 965835 024074 156419 933096 500036 097443 722507 371948 392495 711180 988421 034814 438541 473370 544624 641254 359154 541638 746116 220447 149591 489895 173641 971908 414418 668646 962216 765734 700720 151680 956498 099437 311138 522582 040056 539442 126629 186948 476101 011922 555871 347095 872111 136908 020173 389271 517598 992488 949586 837554 579534 584901 760284 241822 460072 825725 587162 194702 457037 125754 206307 986256 509353 624249 445040 067647 496813 347783 820967 762840 269241 425912 315729 081421 794279 490480 365567 937315 028353 333682 998429 665701 016753 747722 336857 427409 815993 392076 429059 239702 691917 668070 214756 838769 315451 783284 264372 552183 670656 654021 547665 879746 437529 846431 884577 447501 841693 696766 714136 874527 304782 776342 157774 935074 737747 103379 603012 527756 329339 673983 437649 165884 631341 736830 981791 388741 579868 159890 277911 512961 952274 170852 561906 272835 685470 606595 821607 279501 456030 700906 577962 925105 347654 389191 890499 763616 387505 736786 384338 586920 096122 978289 333175 735256 889073 120630 100485 822789 330869 343599 944377 550508 171940 814175 998810 837873 564380 301244 335024 486804 693429 303660 071245 400934 045794 728830 564594 955577 541890 022757 055764 700118 910407 731295 699413 498227 352651 208599 882735 594469 414076 518144 673771 754919 337246 472820 230693 448436 283239 545485 646103 350853 565234 884718 020707 798208 241214 216909 455879 639566 515065 171106 414757 / 2917 > 812951 [i]
- extracting embedded OOA [i] would yield OA(812951, 2953, S81, 2916), but