Best Known (19, 41, s)-Nets in Base 49
(19, 41, 151)-Net over F49 — Constructive and digital
Digital (19, 41, 151)-net over F49, using
- 1 times m-reduction [i] based on digital (19, 42, 151)-net over F49, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 7, 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, 11, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (1, 24, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (0, 7, 50)-net over F49, using
- generalized (u, u+v)-construction [i] based on
(19, 41, 407)-Net over F49 — Digital
Digital (19, 41, 407)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4941, 407, F49, 22) (dual of [407, 366, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4941, 480, F49, 22) (dual of [480, 439, 23]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 480 | 492−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(4941, 480, F49, 22) (dual of [480, 439, 23]-code), using
(19, 41, 203978)-Net in Base 49 — Upper bound on s
There is no (19, 41, 203979)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 1986 371159 322743 639787 476873 154902 457107 019438 133739 658177 043898 269873 > 4941 [i]