Best Known (14, 14+10, s)-Nets in Base 49
(14, 14+10, 530)-Net over F49 — Constructive and digital
Digital (14, 24, 530)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 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 (9, 19, 480)-net over F49, using
- net defined by OOA [i] based on linear OOA(4919, 480, F49, 10, 10) (dual of [(480, 10), 4781, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(4919, 2400, F49, 10) (dual of [2400, 2381, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(4919, 2401, F49, 10) (dual of [2401, 2382, 11]-code), using
- an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(4919, 2401, F49, 10) (dual of [2401, 2382, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(4919, 2400, F49, 10) (dual of [2400, 2381, 11]-code), using
- net defined by OOA [i] based on linear OOA(4919, 480, F49, 10, 10) (dual of [(480, 10), 4781, 11]-NRT-code), using
- digital (0, 5, 50)-net over F49, using
(14, 14+10, 2978)-Net over F49 — Digital
Digital (14, 24, 2978)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4924, 2978, F49, 10) (dual of [2978, 2954, 11]-code), using
- 570 step Varšamov–Edel lengthening with (ri) = (2, 1, 12 times 0, 1, 87 times 0, 1, 467 times 0) [i] based on linear OA(4919, 2403, F49, 10) (dual of [2403, 2384, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(4919, 2401, F49, 10) (dual of [2401, 2382, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 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(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(9) ⊂ Ce(8) [i] based on
- 570 step Varšamov–Edel lengthening with (ri) = (2, 1, 12 times 0, 1, 87 times 0, 1, 467 times 0) [i] based on linear OA(4919, 2403, F49, 10) (dual of [2403, 2384, 11]-code), using
(14, 14+10, 7039406)-Net in Base 49 — Upper bound on s
There is no (14, 24, 7039407)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 36703 372248 201182 079393 641681 364601 349137 > 4924 [i]