Best Known (18, 38, s)-Nets in Base 49
(18, 38, 152)-Net over F49 — Constructive and digital
Digital (18, 38, 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, 11, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (1, 21, 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
(18, 38, 461)-Net over F49 — Digital
Digital (18, 38, 461)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4938, 461, F49, 20) (dual of [461, 423, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4938, 481, F49, 20) (dual of [481, 443, 21]-code), using
- an extension Ce(19) of the narrow-sense BCH-code C(I) with length 480 | 492−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(4938, 481, F49, 20) (dual of [481, 443, 21]-code), using
(18, 38, 249730)-Net in Base 49 — Upper bound on s
There is no (18, 38, 249731)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 16883 239535 973562 860032 952605 086941 299277 711403 211044 071822 381985 > 4938 [i]