Best Known (36−19, 36, s)-Nets in Base 49
(36−19, 36, 152)-Net over F49 — Constructive and digital
Digital (17, 36, 152)-net over F49, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 6, 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 (1, 10, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (1, 20, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49 (see above)
- digital (0, 6, 50)-net over F49, using
(36−19, 36, 444)-Net over F49 — Digital
Digital (17, 36, 444)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4936, 444, F49, 19) (dual of [444, 408, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4936, 481, F49, 19) (dual of [481, 445, 20]-code), using
- an extension Ce(18) of the narrow-sense BCH-code C(I) with length 480 | 492−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(4936, 481, F49, 19) (dual of [481, 445, 20]-code), using
(36−19, 36, 323213)-Net in Base 49 — Upper bound on s
There is no (17, 36, 323214)-net in base 49, because
- 1 times m-reduction [i] would yield (17, 35, 323214)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 143506 052546 849393 105447 762132 755300 422369 225456 211714 667425 > 4935 [i]