Best Known (64, ∞, s)-Nets in Base 5
(64, ∞, 82)-Net over F5 — Constructive and digital
Digital (64, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (64, 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
(64, ∞, 120)-Net over F5 — Digital
Digital (64, m, 120)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (64, 119)-sequence over F5, using
- t-expansion [i] based on digital (61, 119)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 61 and N(F) ≥ 120, using
- t-expansion [i] based on digital (61, 119)-sequence over F5, using
(64, ∞, 273)-Net in Base 5 — Upper bound on s
There is no (64, m, 274)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (64, 1091, 274)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51091, 274, S5, 4, 1027), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1149 673629 620210 235396 221022 222957 752772 088926 676704 812239 102425 862930 524577 435831 595737 076494 590588 957503 908020 865966 094456 713078 754895 308697 710516 229923 040989 087810 692176 653907 722276 582290 188153 267358 276347 233679 737321 868500 974974 344789 414446 292008 730443 821851 422677 555438 328617 117023 508508 019492 033305 849434 258010 061192 354151 213343 850699 428086 580246 294737 864986 889265 901865 057142 406670 012008 514792 862701 793607 085789 515287 601644 829674 343723 365523 609948 557028 034186 947882 986182 989040 263284 103781 262804 035035 902658 335502 152856 426001 658931 413338 028420 272575 411137 996412 514192 024311 719781 600199 324308 595535 645802 844134 112034 964077 556693 261555 437138 784893 143471 940254 519553 182749 227727 533001 009170 001459 148535 952835 916438 958510 817081 037913 567342 911846 935749 053955 078125 / 257 > 51091 [i]
- extracting embedded OOA [i] would yield OOA(51091, 274, S5, 4, 1027), but