Best Known (49, 66, s)-Nets in Base 4
(49, 66, 514)-Net over F4 — Constructive and digital
Digital (49, 66, 514)-net over F4, using
- trace code for nets [i] based on digital (16, 33, 257)-net over F16, using
- base reduction for projective spaces (embedding PG(16,256) in PG(32,16)) for nets [i] based on digital (0, 17, 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
- base reduction for projective spaces (embedding PG(16,256) in PG(32,16)) for nets [i] based on digital (0, 17, 257)-net over F256, using
(49, 66, 859)-Net over F4 — Digital
Digital (49, 66, 859)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(466, 859, F4, 17) (dual of [859, 793, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(466, 1023, F4, 17) (dual of [1023, 957, 18]-code), using
(49, 66, 97786)-Net in Base 4 — Upper bound on s
There is no (49, 66, 97787)-net in base 4, because
- 1 times m-reduction [i] would yield (49, 65, 97787)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 1361 186345 006612 205100 881433 460445 638695 > 465 [i]