Best Known (56−49, 56, s)-Nets in Base 128
(56−49, 56, 216)-Net over F128 — Constructive and digital
Digital (7, 56, 216)-net over F128, using
- t-expansion [i] based on digital (5, 56, 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
(56−49, 56, 257)-Net in Base 128 — Constructive
(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
(56−49, 56, 262)-Net over F128 — Digital
Digital (7, 56, 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
(56−49, 56, 5195)-Net in Base 128 — Upper bound on s
There is no (7, 56, 5196)-net in base 128, because
- 1 times m-reduction [i] would yield (7, 55, 5196)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 79 077787 494479 547203 329637 965720 519582 036510 763498 047192 858396 212975 363163 072846 896164 367435 438024 218063 918033 084276 > 12855 [i]