Best Known (18, 18+33, s)-Nets in Base 128
(18, 18+33, 300)-Net over F128 — Constructive and digital
Digital (18, 51, 300)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 17, 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 (1, 34, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128 (see above)
- digital (1, 17, 150)-net over F128, using
(18, 18+33, 386)-Net over F128 — Digital
Digital (18, 51, 386)-net over F128, using
- t-expansion [i] based on digital (15, 51, 386)-net over F128, using
- net from sequence [i] based on digital (15, 385)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 15 and N(F) ≥ 386, using
- net from sequence [i] based on digital (15, 385)-sequence over F128, using
(18, 18+33, 513)-Net in Base 128
(18, 51, 513)-net in base 128, using
- t-expansion [i] based on (17, 51, 513)-net in base 128, using
- 21 times m-reduction [i] based on (17, 72, 513)-net in base 128, using
- base change [i] based on digital (8, 63, 513)-net over F256, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- base change [i] based on digital (8, 63, 513)-net over F256, using
- 21 times m-reduction [i] based on (17, 72, 513)-net in base 128, using
(18, 18+33, 205944)-Net in Base 128 — Upper bound on s
There is no (18, 51, 205945)-net in base 128, because
- 1 times m-reduction [i] would yield (18, 50, 205945)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 2293 597887 397324 541007 027116 371706 951414 537244 306651 425239 963320 286102 203772 688931 587518 104618 009915 480045 > 12850 [i]