Best Known (13, 13+15, s)-Nets in Base 128
(13, 13+15, 408)-Net over F128 — Constructive and digital
Digital (13, 28, 408)-net over F128, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 5, 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 (0, 7, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128 (see above)
- digital (1, 16, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- digital (0, 5, 129)-net over F128, using
(13, 13+15, 516)-Net in Base 128 — Constructive
(13, 28, 516)-net in base 128, using
- (u, u+v)-construction [i] based on
- (1, 8, 257)-net in base 128, using
- base change [i] based on digital (0, 7, 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, 7, 257)-net over F256, using
- (5, 20, 259)-net in base 128, using
- 4 times m-reduction [i] based on (5, 24, 259)-net in base 128, using
- base change [i] based on digital (2, 21, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- base change [i] based on digital (2, 21, 259)-net over F256, using
- 4 times m-reduction [i] based on (5, 24, 259)-net in base 128, using
- (1, 8, 257)-net in base 128, using
(13, 13+15, 787)-Net over F128 — Digital
Digital (13, 28, 787)-net over F128, using
(13, 13+15, 3572106)-Net in Base 128 — Upper bound on s
There is no (13, 28, 3572107)-net in base 128, because
- 1 times m-reduction [i] would yield (13, 27, 3572107)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 784 637980 063293 493253 205366 653110 696500 175353 929265 384200 > 12827 [i]