Best Known (57−28, 57, s)-Nets in Base 4
(57−28, 57, 44)-Net over F4 — Constructive and digital
Digital (29, 57, 44)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 19, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- digital (10, 38, 27)-net over F4, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 10 and N(F) ≥ 27, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- digital (5, 19, 17)-net over F4, using
(57−28, 57, 46)-Net in Base 4 — Constructive
(29, 57, 46)-net in base 4, using
- base change [i] based on digital (10, 38, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
(57−28, 57, 56)-Net over F4 — Digital
Digital (29, 57, 56)-net over F4, using
(57−28, 57, 558)-Net in Base 4 — Upper bound on s
There is no (29, 57, 559)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 21009 458378 501477 472521 108203 730845 > 457 [i]