Best Known (66, 66+46, s)-Nets in Base 5
(66, 66+46, 252)-Net over F5 — Constructive and digital
Digital (66, 112, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 56, 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
(66, 66+46, 5954)-Net in Base 5 — Upper bound on s
There is no (66, 112, 5955)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1 928387 566686 000713 412997 410591 351830 691951 997977 722790 514955 820804 346209 646965 > 5112 [i]