Best Known (23−18, 23, s)-Nets in Base 128
(23−18, 23, 216)-Net over F128 — Constructive and digital
Digital (5, 23, 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
(23−18, 23, 227)-Net over F128 — Digital
Digital (5, 23, 227)-net over F128, using
- net from sequence [i] based on digital (5, 226)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 227, using
(23−18, 23, 259)-Net in Base 128 — Constructive
(5, 23, 259)-net in base 128, using
- 1 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
(23−18, 23, 321)-Net in Base 128
(5, 23, 321)-net in base 128, using
- 1 times m-reduction [i] based on (5, 24, 321)-net in base 128, using
- base change [i] based on digital (2, 21, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 21, 321)-net over F256, using
(23−18, 23, 7921)-Net in Base 128 — Upper bound on s
There is no (5, 23, 7922)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 2 924097 096339 533178 057011 120747 403711 811487 894022 > 12823 [i]