Best Known (119, ∞, s)-Nets in Base 5
(119, ∞, 102)-Net over F5 — Constructive and digital
Digital (119, m, 102)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (119, 101)-sequence over F5, using
- base reduction for sequences [i] based on digital (9, 101)-sequence over F25, using
- s-reduction 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
- s-reduction based on digital (9, 103)-sequence over F25, using
- base reduction for sequences [i] based on digital (9, 101)-sequence over F25, using
(119, ∞, 195)-Net over F5 — Digital
Digital (119, m, 195)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (119, 194)-sequence over F5, using
- t-expansion [i] based on digital (118, 194)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 118 and N(F) ≥ 195, using
- t-expansion [i] based on digital (118, 194)-sequence over F5, using
(119, ∞, 495)-Net in Base 5 — Upper bound on s
There is no (119, m, 496)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (119, 1979, 496)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51979, 496, S5, 4, 1860), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4 575581 666462 741880 597301 368333 758649 047880 538621 633832 616869 345863 813264 107414 460098 049856 399677 826965 278669 066369 777468 690509 844569 030916 955416 248279 149017 732855 189258 852322 815301 145925 616529 674471 830123 685500 359809 328307 956804 726401 232838 536740 276636 360564 571829 254280 133125 275067 122463 810220 406537 944159 008623 881048 185906 173722 842779 344555 976546 370495 913617 726890 894069 592868 056068 711957 235845 856268 431009 292754 855031 973644 681403 277989 257570 153712 687004 661267 679094 376703 706163 904174 993092 992182 460513 456945 152172 274089 678736 699975 269255 599129 795560 137920 673008 620871 962658 874206 330608 620250 114915 435599 037228 657636 514169 970971 612986 592197 664639 554896 881460 537440 196659 774891 786149 115271 752165 551824 810891 512820 159401 446165 639170 784714 026051 318589 306883 007292 734332 412937 166927 608975 630192 841530 548734 881418 612522 732761 066669 837072 377065 620075 124340 140381 501201 740689 071492 098668 168653 568654 586875 004337 442968 207184 989382 430600 105298 698482 128269 739678 708516 804280 247043 661586 968265 830513 473345 886024 741208 238501 024510 416453 059636 933005 950054 685755 251366 978345 423971 547645 969122 480541 947708 287535 695143 203771 969820 290212 116492 194792 868958 715506 206515 340150 010981 332960 150320 328499 063491 828673 346640 338521 228126 653223 207065 428053 393878 548507 905046 122780 892923 112895 452035 905059 333492 178478 351626 297899 882949 086411 034373 767341 283675 878832 982943 274221 288021 408327 040262 520313 262939 453125 / 1861 > 51979 [i]
- extracting embedded OOA [i] would yield OOA(51979, 496, S5, 4, 1860), but