Best Known (21−12, 21, s)-Nets in Base 49
(21−12, 21, 103)-Net over F49 — Constructive and digital
Digital (9, 21, 103)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (2, 14, 52)-net over F49, using
- net from sequence [i] based on digital (2, 51)-sequence over F49, using
- digital (1, 7, 51)-net over F49, using
(21−12, 21, 223)-Net over F49 — Digital
Digital (9, 21, 223)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4921, 223, F49, 12) (dual of [223, 202, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(4921, 241, F49, 12) (dual of [241, 220, 13]-code), using
- an extension Ce(11) of the narrow-sense BCH-code C(I) with length 240 | 492−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(4921, 241, F49, 12) (dual of [241, 220, 13]-code), using
(21−12, 21, 51362)-Net in Base 49 — Upper bound on s
There is no (9, 21, 51363)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 311996 977717 996849 106968 225620 734305 > 4921 [i]