Best Known (8, 8+6, s)-Nets in Base 49
(8, 8+6, 2450)-Net over F49 — Constructive and digital
Digital (8, 14, 2450)-net over F49, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 0, 50)-net over F49, using
- s-reduction based on digital (0, 0, s)-net over F49 with arbitrarily large s, using
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 0, 50)-net over F49 (see above)
- digital (0, 1, 50)-net over F49, using
- s-reduction based on digital (0, 1, s)-net over F49 with arbitrarily large s, using
- digital (0, 1, 50)-net over F49 (see above)
- digital (0, 1, 50)-net over F49 (see above)
- digital (0, 2, 50)-net over F49, using
- 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, 6, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (0, 0, 50)-net over F49, using
(8, 8+6, 3253)-Net over F49 — Digital
Digital (8, 14, 3253)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4914, 3253, F49, 6) (dual of [3253, 3239, 7]-code), using
- 847 step Varšamov–Edel lengthening with (ri) = (2, 44 times 0, 1, 801 times 0) [i] based on linear OA(4911, 2403, F49, 6) (dual of [2403, 2392, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(4911, 2401, F49, 6) (dual of [2401, 2390, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(499, 2401, F49, 5) (dual of [2401, 2392, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- 847 step Varšamov–Edel lengthening with (ri) = (2, 44 times 0, 1, 801 times 0) [i] based on linear OA(4911, 2403, F49, 6) (dual of [2403, 2392, 7]-code), using
(8, 8+6, 2922295)-Net in Base 49 — Upper bound on s
There is no (8, 14, 2922296)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 459986 987618 114438 521729 > 4914 [i]