Best Known (15, 25, s)-Nets in Base 49
(15, 25, 531)-Net over F49 — Constructive and digital
Digital (15, 25, 531)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-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 (1, 6, 51)-net over F49, using
(15, 25, 4306)-Net over F49 — Digital
Digital (15, 25, 4306)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4925, 4306, F49, 10) (dual of [4306, 4281, 11]-code), using
- 1897 step Varšamov–Edel lengthening with (ri) = (2, 1, 12 times 0, 1, 87 times 0, 1, 467 times 0, 1, 1326 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
- 1897 step Varšamov–Edel lengthening with (ri) = (2, 1, 12 times 0, 1, 87 times 0, 1, 467 times 0, 1, 1326 times 0) [i] based on linear OA(4919, 2403, F49, 10) (dual of [2403, 2384, 11]-code), using
(15, 25, large)-Net in Base 49 — Upper bound on s
There is no (15, 25, large)-net in base 49, because
- 8 times m-reduction [i] would yield (15, 17, large)-net in base 49, but