Best Known (56−18, 56, s)-Nets in Base 5
(56−18, 56, 252)-Net over F5 — Constructive and digital
Digital (38, 56, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 28, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(56−18, 56, 368)-Net over F5 — Digital
Digital (38, 56, 368)-net over F5, using
(56−18, 56, 23159)-Net in Base 5 — Upper bound on s
There is no (38, 56, 23160)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1388 284361 779803 906017 471737 979078 681569 > 556 [i]