Best Known (65−41, 65, s)-Nets in Base 128
(65−41, 65, 342)-Net over F128 — Constructive and digital
Digital (24, 65, 342)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 21, 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 (3, 44, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- digital (1, 21, 150)-net over F128, using
(65−41, 65, 513)-Net over F128 — Digital
Digital (24, 65, 513)-net over F128, using
- net from sequence [i] based on digital (24, 512)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 24 and N(F) ≥ 513, using
(65−41, 65, 361878)-Net in Base 128 — Upper bound on s
There is no (24, 65, 361879)-net in base 128, because
- 1 times m-reduction [i] would yield (24, 64, 361879)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 726 857421 955787 428826 923816 644653 883274 625045 267272 771084 151790 758674 612117 099090 610804 852631 621317 784850 380606 497752 152752 294295 068671 > 12864 [i]