Best Known (91, 91+∞, s)-Nets in Base 5
(91, 91+∞, 82)-Net over F5 — Constructive and digital
Digital (91, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (91, 81)-sequence over F5, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
(91, 91+∞, 150)-Net over F5 — Digital
Digital (91, m, 150)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (91, 149)-sequence over F5, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 76 and N(F) ≥ 150, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
(91, 91+∞, 382)-Net in Base 5 — Upper bound on s
There is no (91, m, 383)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (91, 1527, 383)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51527, 383, S5, 4, 1436), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 396 164409 781422 944942 201429 726891 920467 011629 509799 414784 930881 776168 120223 656209 561703 878652 446549 054647 379233 383628 914316 425912 304453 359799 025317 848000 949217 893528 616851 553180 732273 891184 972752 384270 336484 100035 223083 888670 590367 681526 359765 869538 949884 335859 917490 882240 505935 293951 631290 967273 573634 407069 551517 649391 795019 955090 169068 527758 940257 961755 299767 934567 600917 696935 825293 188103 559984 346587 394983 039987 439971 037975 716406 559886 348532 724124 894489 160900 876379 309809 000934 796957 925052 466595 823763 434310 096486 862589 686731 482810 664769 664133 482660 718783 854169 824144 730694 155237 029448 365067 297990 676064 976801 433916 516635 230953 522891 175410 530802 906783 815357 713376 720946 931722 256673 043443 539067 355025 970347 613694 902027 243371 275272 343878 451092 478487 283232 890913 514659 477935 480378 605171 827682 019131 758674 854341 082692 947266 221890 109251 326710 914334 683843 115131 188752 018891 017687 089003 921155 773033 613797 184492 688556 599514 807519 015222 916429 290348 046619 896190 481756 292304 288358 677174 601536 882347 101638 499380 613176 435722 680859 702620 088935 720588 096955 907531 082630 157470 703125 / 1437 > 51527 [i]
- extracting embedded OOA [i] would yield OOA(51527, 383, S5, 4, 1436), but