Best Known (14, 14+9, s)-Nets in Base 49
(14, 14+9, 2450)-Net over F49 — Constructive and digital
Digital (14, 23, 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, 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, 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, 4, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (0, 9, 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
(14, 14+9, 5685)-Net over F49 — Digital
Digital (14, 23, 5685)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4923, 5685, F49, 9) (dual of [5685, 5662, 10]-code), using
- 3276 step Varšamov–Edel lengthening with (ri) = (2, 4 times 0, 1, 32 times 0, 1, 216 times 0, 1, 926 times 0, 1, 2093 times 0) [i] based on linear OA(4917, 2403, F49, 9) (dual of [2403, 2386, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(4917, 2401, F49, 9) (dual of [2401, 2384, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(4915, 2401, F49, 8) (dual of [2401, 2386, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(8) ⊂ Ce(7) [i] based on
- 3276 step Varšamov–Edel lengthening with (ri) = (2, 4 times 0, 1, 32 times 0, 1, 216 times 0, 1, 926 times 0, 1, 2093 times 0) [i] based on linear OA(4917, 2403, F49, 9) (dual of [2403, 2386, 10]-code), using
(14, 14+9, large)-Net in Base 49 — Upper bound on s
There is no (14, 23, large)-net in base 49, because
- 7 times m-reduction [i] would yield (14, 16, large)-net in base 49, but