Best Known (28, 28+13, s)-Nets in Base 4
(28, 28+13, 195)-Net over F4 — Constructive and digital
Digital (28, 41, 195)-net over F4, using
- 1 times m-reduction [i] based on digital (28, 42, 195)-net over F4, using
- trace code for nets [i] based on digital (0, 14, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 14, 65)-net over F64, using
(28, 28+13, 246)-Net over F4 — Digital
Digital (28, 41, 246)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(441, 246, F4, 13) (dual of [246, 205, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(441, 255, F4, 13) (dual of [255, 214, 14]-code), using
(28, 28+13, 10295)-Net in Base 4 — Upper bound on s
There is no (28, 41, 10296)-net in base 4, because
- 1 times m-reduction [i] would yield (28, 40, 10296)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 1 209329 566919 010280 939339 > 440 [i]