Best Known (43, 66, s)-Nets in Base 5
(43, 66, 252)-Net over F5 — Constructive and digital
Digital (43, 66, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 33, 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
(43, 66, 294)-Net over F5 — Digital
Digital (43, 66, 294)-net over F5, using
(43, 66, 16558)-Net in Base 5 — Upper bound on s
There is no (43, 66, 16559)-net in base 5, because
- 1 times m-reduction [i] would yield (43, 65, 16559)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 2710 905039 571958 854588 990090 271685 728400 532885 > 565 [i]