Best Known (12, 26, s)-Nets in Base 49
(12, 26, 151)-Net over F49 — Constructive and digital
Digital (12, 26, 151)-net over F49, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 4, 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, 15, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (0, 4, 50)-net over F49, using
(12, 26, 361)-Net over F49 — Digital
Digital (12, 26, 361)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4926, 361, F49, 14) (dual of [361, 335, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(4926, 480, F49, 14) (dual of [480, 454, 15]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 480 | 492−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(4926, 480, F49, 14) (dual of [480, 454, 15]-code), using
(12, 26, 133517)-Net in Base 49 — Upper bound on s
There is no (12, 26, 133518)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 88 126897 147932 124904 613374 877946 679734 816609 > 4926 [i]