Best Known (78, ∞, s)-Nets in Base 9
(78, ∞, 165)-Net over F9 — Constructive and digital
Digital (78, m, 165)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (78, 164)-sequence over F9, using
- t-expansion [i] based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- t-expansion [i] based on digital (64, 164)-sequence over F9, using
(78, ∞, 192)-Net over F9 — Digital
Digital (78, m, 192)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (78, 191)-sequence over F9, using
- t-expansion [i] based on digital (61, 191)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 61 and N(F) ≥ 192, using
- t-expansion [i] based on digital (61, 191)-sequence over F9, using
(78, ∞, 651)-Net in Base 9 — Upper bound on s
There is no (78, m, 652)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (78, 1952, 652)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(91952, 652, S9, 3, 1874), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 407648 750797 441372 971473 336975 860525 538429 649756 207746 880451 778084 041243 747906 819725 653626 220931 528444 498608 176563 471792 186477 191995 464595 900231 613133 981911 097633 852089 836388 775386 772680 461058 837510 099245 433866 485071 150925 637212 481652 109613 204503 938320 422866 053911 232391 376752 573908 811892 288395 121860 876443 176444 131130 706201 009785 186657 746376 964619 848942 162186 686177 520813 539177 583988 656589 836637 303424 510203 649492 336061 315788 386008 374437 018672 246383 950893 024423 573719 190264 543195 587588 921092 534558 537539 427549 547781 219102 784098 531032 579270 357235 623443 753848 239948 573548 733012 889771 937435 059214 612426 043052 901830 282687 783227 584142 007245 396586 963171 907175 686033 338523 844666 034319 493341 431768 736113 226163 717056 449367 313641 125637 798989 473045 102069 864580 680506 747006 930917 348545 320299 171656 931840 832970 564880 620327 808408 369383 729356 924858 508135 209719 733239 267287 846729 510307 360071 420733 948649 138752 129838 557697 992498 716241 781185 151693 510623 829495 999130 760137 458384 608007 437501 630130 788691 127473 208431 029096 410877 745685 380043 887075 800673 311296 145060 038293 349665 570934 028719 560598 852386 732930 760839 926006 379435 166034 095078 032707 598339 355059 621346 175474 350403 437490 878758 604372 620465 840036 993602 025662 790753 332501 038509 708000 836049 824356 177054 769221 608877 385362 086120 441945 943395 834859 454130 268153 128178 267940 444324 109289 906695 484514 088615 230106 455019 513569 969649 999407 885628 506387 097903 164981 752828 188737 544536 268239 705609 943288 282072 979587 955960 035200 420770 913478 608235 881278 261684 896135 700844 397280 735872 654367 461827 946416 524402 696771 445699 963904 612929 638181 923454 045903 150177 064471 506430 411185 854069 402614 088617 090564 257139 020157 432587 987694 589970 169929 867016 176635 738430 091311 216826 713655 656171 793216 832462 267728 118590 397037 455641 922225 549159 143998 864139 780560 623079 153388 248050 969120 403678 844183 695344 192582 959001 577033 479108 145880 133551 666185 473759 523759 432272 370769 / 625 > 91952 [i]
- extracting embedded OOA [i] would yield OOA(91952, 652, S9, 3, 1874), but