Best Known (8, 19, s)-Nets in Base 49
(8, 19, 150)-Net over F49 — Constructive and digital
Digital (8, 19, 150)-net over F49, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 3, 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, 5, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (0, 11, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (0, 3, 50)-net over F49, using
(8, 19, 204)-Net over F49 — Digital
Digital (8, 19, 204)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4919, 204, F49, 11) (dual of [204, 185, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(4919, 241, F49, 11) (dual of [241, 222, 12]-code), using
- an extension Ce(10) of the narrow-sense BCH-code C(I) with length 240 | 492−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(4919, 241, F49, 11) (dual of [241, 222, 12]-code), using
(8, 19, 65960)-Net in Base 49 — Upper bound on s
There is no (8, 19, 65961)-net in base 49, because
- 1 times m-reduction [i] would yield (8, 18, 65961)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 2 651736 491281 591621 810618 376305 > 4918 [i]