Best Known (13, 13+15, s)-Nets in Base 49
(13, 13+15, 151)-Net over F49 — Constructive and digital
Digital (13, 28, 151)-net over F49, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 5, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- digital (0, 7, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (1, 16, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (0, 5, 50)-net over F49, using
(13, 13+15, 377)-Net over F49 — Digital
Digital (13, 28, 377)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4928, 377, F49, 15) (dual of [377, 349, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(4928, 480, F49, 15) (dual of [480, 452, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 480 | 492−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(4928, 480, F49, 15) (dual of [480, 452, 16]-code), using
(13, 13+15, 232808)-Net in Base 49 — Upper bound on s
There is no (13, 28, 232809)-net in base 49, because
- 1 times m-reduction [i] would yield (13, 27, 232809)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 4318 148378 803576 804865 023920 160183 276313 309905 > 4927 [i]