Best Known (42, 42+22, s)-Nets in Base 5
(42, 42+22, 252)-Net over F5 — Constructive and digital
Digital (42, 64, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 32, 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
(42, 42+22, 303)-Net over F5 — Digital
Digital (42, 64, 303)-net over F5, using
(42, 42+22, 14303)-Net in Base 5 — Upper bound on s
There is no (42, 64, 14304)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 542 155444 543237 570860 928436 667227 125821 012865 > 564 [i]