Best Known (78−71, 78, s)-Nets in Base 128
(78−71, 78, 216)-Net over F128 — Constructive and digital
Digital (7, 78, 216)-net over F128, using
- t-expansion [i] based on digital (5, 78, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
(78−71, 78, 262)-Net over F128 — Digital
Digital (7, 78, 262)-net over F128, using
- net from sequence [i] based on digital (7, 261)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 7 and N(F) ≥ 262, using
(78−71, 78, 4717)-Net in Base 128 — Upper bound on s
There is no (7, 78, 4718)-net in base 128, because
- 1 times m-reduction [i] would yield (7, 77, 4718)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 1 802784 898376 082119 773612 363939 844359 711468 005928 256690 001881 783398 068921 884919 081534 560228 433412 075882 461356 230617 561020 267638 284032 807451 353164 216341 094721 931958 > 12877 [i]