Best Known (25, 25+12, s)-Nets in Base 49
(25, 25+12, 19610)-Net over F49 — Constructive and digital
Digital (25, 37, 19610)-net over F49, using
- 491 times duplication [i] based on digital (24, 36, 19610)-net over F49, using
- net defined by OOA [i] based on linear OOA(4936, 19610, F49, 12, 12) (dual of [(19610, 12), 235284, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(4936, 117660, F49, 12) (dual of [117660, 117624, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(4934, 117649, F49, 12) (dual of [117649, 117615, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(4925, 117649, F49, 9) (dual of [117649, 117624, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(492, 11, F49, 2) (dual of [11, 9, 3]-code or 11-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(11) ⊂ Ce(8) [i] based on
- OA 6-folding and stacking [i] based on linear OA(4936, 117660, F49, 12) (dual of [117660, 117624, 13]-code), using
- net defined by OOA [i] based on linear OOA(4936, 19610, F49, 12, 12) (dual of [(19610, 12), 235284, 13]-NRT-code), using
(25, 25+12, 114663)-Net over F49 — Digital
Digital (25, 37, 114663)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4937, 114663, F49, 12) (dual of [114663, 114626, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(4937, 117664, F49, 12) (dual of [117664, 117627, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- linear OA(4934, 117649, F49, 12) (dual of [117649, 117615, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(4922, 117649, F49, 8) (dual of [117649, 117627, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(493, 15, F49, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,49) or 15-cap in PG(2,49)), using
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
- Reed–Solomon code RS(46,49) [i]
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(4937, 117664, F49, 12) (dual of [117664, 117627, 13]-code), using
(25, 25+12, large)-Net in Base 49 — Upper bound on s
There is no (25, 37, large)-net in base 49, because
- 10 times m-reduction [i] would yield (25, 27, large)-net in base 49, but