Best Known (23, 31, s)-Nets in Base 4
(23, 31, 514)-Net over F4 — Constructive and digital
Digital (23, 31, 514)-net over F4, using
- base reduction for projective spaces (embedding PG(15,16) in PG(30,4)) for nets [i] based on digital (8, 16, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 8, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 8, 257)-net over F256, using
(23, 31, 1018)-Net over F4 — Digital
Digital (23, 31, 1018)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(431, 1018, F4, 8) (dual of [1018, 987, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(431, 1023, F4, 8) (dual of [1023, 992, 9]-code), using
(23, 31, 34186)-Net in Base 4 — Upper bound on s
There is no (23, 31, 34187)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 4 611707 001422 874034 > 431 [i]