Best Known (122, ∞, s)-Nets in Base 5
(122, ∞, 104)-Net over F5 — Constructive and digital
Digital (122, m, 104)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (122, 103)-sequence over F5, using
- t-expansion [i] based on digital (121, 103)-sequence over F5, using
- base reduction for sequences [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- base reduction for sequences [i] based on digital (9, 103)-sequence over F25, using
- t-expansion [i] based on digital (121, 103)-sequence over F5, using
(122, ∞, 200)-Net over F5 — Digital
Digital (122, m, 200)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (122, 199)-sequence over F5, using
- t-expansion [i] based on digital (121, 199)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 121 and N(F) ≥ 200, using
- t-expansion [i] based on digital (121, 199)-sequence over F5, using
(122, ∞, 507)-Net in Base 5 — Upper bound on s
There is no (122, m, 508)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (122, 2027, 508)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(52027, 508, S5, 4, 1905), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 8079 195932 440783 650496 872805 803787 714499 670386 067188 402802 608214 859194 772311 153210 820257 473547 559910 957982 606095 024664 098079 768160 824089 292234 237921 633706 161432 996950 802445 531984 715058 371750 438728 059017 552998 343298 089236 904664 281122 132340 044201 390748 213369 029034 655648 992831 617114 530545 175498 309331 690414 819079 358864 462822 747741 629334 812929 767868 884659 915603 294548 420706 173388 085016 469923 708553 397074 691533 878312 432600 781738 613916 175071 513576 990083 259011 941464 959057 758240 092786 403476 853397 189049 846586 813730 871436 576762 735237 727559 056175 625408 691566 777532 917301 575006 905593 186666 345686 700985 739308 135209 511650 465783 276643 637420 648895 805295 995598 980040 070612 604050 635763 238811 317052 459199 767182 056478 983858 159478 875977 289383 806873 547943 274381 231564 856664 372500 258847 887723 538640 805435 259616 924969 465927 736762 364016 323558 684393 135855 977021 218737 646039 898654 958213 864222 633031 023515 695344 747945 124348 755267 967115 349124 133253 171612 365907 196953 315023 611818 538289 380209 782787 652058 257520 836912 812458 297542 454112 279969 186640 445152 353767 386355 396203 427891 178889 826311 197431 429643 479676 988676 365705 122479 936933 943444 845138 614768 234136 179332 770686 053704 746729 361864 421843 927129 316663 773662 504020 815124 750259 746256 559864 261712 689417 222405 280736 074169 511228 064581 272653 840236 622764 638635 266552 220873 024774 564920 636025 490343 336155 178830 470181 864724 522036 899187 620081 482699 668830 349307 475252 075561 034104 111968 190409 243106 842041 015625 / 953 > 52027 [i]
- extracting embedded OOA [i] would yield OOA(52027, 508, S5, 4, 1905), but