Best Known (31, 31+45, s)-Nets in Base 128
(31, 31+45, 417)-Net over F128 — Constructive and digital
Digital (31, 76, 417)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 22, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (9, 54, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- digital (0, 22, 129)-net over F128, using
(31, 31+45, 432)-Net in Base 128 — Constructive
(31, 76, 432)-net in base 128, using
- (u, u+v)-construction [i] based on
- (4, 26, 257)-net in base 128, using
- 6 times m-reduction [i] based on (4, 32, 257)-net in base 128, using
- base change [i] based on digital (0, 28, 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, 28, 257)-net over F256, using
- 6 times m-reduction [i] based on (4, 32, 257)-net in base 128, using
- digital (5, 50, 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
- (4, 26, 257)-net in base 128, using
(31, 31+45, 611)-Net over F128 — Digital
Digital (31, 76, 611)-net over F128, using
(31, 31+45, 1088216)-Net in Base 128 — Upper bound on s
There is no (31, 76, 1088217)-net in base 128, because
- 1 times m-reduction [i] would yield (31, 75, 1088217)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 109 837366 843954 945883 264226 340235 535950 323964 826484 364001 080532 462726 602364 013540 870113 789633 171123 913288 349147 301436 733981 464068 803068 575074 178126 735777 244228 > 12875 [i]