Best Known (86−63, 86, s)-Nets in Base 25
(86−63, 86, 148)-Net over F25 — Constructive and digital
Digital (23, 86, 148)-net over F25, using
- t-expansion [i] based on digital (19, 86, 148)-net over F25, using
- net from sequence [i] based on digital (19, 147)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 19 and N(F) ≥ 148, using
- net from sequence [i] based on digital (19, 147)-sequence over F25, using
(86−63, 86, 176)-Net over F25 — Digital
Digital (23, 86, 176)-net over F25, using
- net from sequence [i] based on digital (23, 175)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 23 and N(F) ≥ 176, using
(86−63, 86, 3506)-Net in Base 25 — Upper bound on s
There is no (23, 86, 3507)-net in base 25, because
- 1 times m-reduction [i] would yield (23, 85, 3507)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 67122 482970 867612 060310 043917 254655 654316 414536 229995 054813 208119 313051 950061 690457 139893 733901 483205 305382 421445 600185 > 2585 [i]