Best Known (26, 35, s)-Nets in Base 49
(26, 35, 1441203)-Net over F49 — Constructive and digital
Digital (26, 35, 1441203)-net over F49, using
- net defined by OOA [i] based on linear OOA(4935, 1441203, F49, 9, 9) (dual of [(1441203, 9), 12970792, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(4935, 5764813, F49, 9) (dual of [5764813, 5764778, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(4935, 5764815, F49, 9) (dual of [5764815, 5764780, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(4933, 5764801, F49, 9) (dual of [5764801, 5764768, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(4921, 5764801, F49, 6) (dual of [5764801, 5764780, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(492, 14, F49, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,49)), using
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- Reed–Solomon code RS(47,49) [i]
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(4935, 5764815, F49, 9) (dual of [5764815, 5764780, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(4935, 5764813, F49, 9) (dual of [5764813, 5764778, 10]-code), using
(26, 35, 5764815)-Net over F49 — Digital
Digital (26, 35, 5764815)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4935, 5764815, F49, 9) (dual of [5764815, 5764780, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(4933, 5764801, F49, 9) (dual of [5764801, 5764768, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(4921, 5764801, F49, 6) (dual of [5764801, 5764780, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(492, 14, F49, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,49)), using
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- Reed–Solomon code RS(47,49) [i]
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
(26, 35, large)-Net in Base 49 — Upper bound on s
There is no (26, 35, large)-net in base 49, because
- 7 times m-reduction [i] would yield (26, 28, large)-net in base 49, but