Best Known (7, 54, s)-Nets in Base 128
(7, 54, 216)-Net over F128 — Constructive and digital
Digital (7, 54, 216)-net over F128, using
- t-expansion [i] based on digital (5, 54, 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
(7, 54, 257)-Net in Base 128 — Constructive
(7, 54, 257)-net in base 128, using
- 2 times m-reduction [i] based on (7, 56, 257)-net in base 128, using
- base change [i] based on digital (0, 49, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 49, 257)-net over F256, using
(7, 54, 262)-Net over F128 — Digital
Digital (7, 54, 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
(7, 54, 5314)-Net in Base 128 — Upper bound on s
There is no (7, 54, 5315)-net in base 128, because
- 1 times m-reduction [i] would yield (7, 53, 5315)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 4814 476557 043205 399259 680066 887209 042083 054603 365199 033596 329222 813443 992989 069064 486916 427600 069770 702889 044544 > 12853 [i]