Best Known (12, 32, s)-Nets in Base 128
(12, 32, 300)-Net over F128 — Constructive and digital
Digital (12, 32, 300)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 11, 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, 21, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128 (see above)
- digital (1, 11, 150)-net over F128, using
(12, 32, 321)-Net over F128 — Digital
Digital (12, 32, 321)-net over F128, using
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 12 and N(F) ≥ 321, using
(12, 32, 513)-Net in Base 128
(12, 32, 513)-net in base 128, using
- base change [i] based on digital (8, 28, 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
(12, 32, 197348)-Net in Base 128 — Upper bound on s
There is no (12, 32, 197349)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 26 960270 025539 004501 384048 052721 047995 363006 549739 859694 578115 148376 > 12832 [i]