Best Known (38, 38+13, s)-Nets in Base 4
(38, 38+13, 514)-Net over F4 — Constructive and digital
Digital (38, 51, 514)-net over F4, using
- base reduction for projective spaces (embedding PG(25,16) in PG(50,4)) for nets [i] based on digital (13, 26, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 13, 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, 13, 257)-net over F256, using
(38, 38+13, 884)-Net over F4 — Digital
Digital (38, 51, 884)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(451, 884, F4, 13) (dual of [884, 833, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(451, 1023, F4, 13) (dual of [1023, 972, 14]-code), using
(38, 38+13, 103812)-Net in Base 4 — Upper bound on s
There is no (38, 51, 103813)-net in base 4, because
- 1 times m-reduction [i] would yield (38, 50, 103813)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 1 267705 659541 607214 964816 354480 > 450 [i]