Best Known (36, 48, s)-Nets in Base 49
(36, 48, 960803)-Net over F49 — Constructive and digital
Digital (36, 48, 960803)-net over F49, using
- net defined by OOA [i] based on linear OOA(4948, 960803, F49, 12, 12) (dual of [(960803, 12), 11529588, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(4948, 5764818, F49, 12) (dual of [5764818, 5764770, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(4948, 5764820, F49, 12) (dual of [5764820, 5764772, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- linear OA(4945, 5764801, F49, 12) (dual of [5764801, 5764756, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(4929, 5764801, F49, 8) (dual of [5764801, 5764772, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(493, 19, F49, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,49) or 19-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(4948, 5764820, F49, 12) (dual of [5764820, 5764772, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(4948, 5764818, F49, 12) (dual of [5764818, 5764770, 13]-code), using
(36, 48, 5764820)-Net over F49 — Digital
Digital (36, 48, 5764820)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4948, 5764820, F49, 12) (dual of [5764820, 5764772, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- linear OA(4945, 5764801, F49, 12) (dual of [5764801, 5764756, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(4929, 5764801, F49, 8) (dual of [5764801, 5764772, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(493, 19, F49, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,49) or 19-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
(36, 48, large)-Net in Base 49 — Upper bound on s
There is no (36, 48, large)-net in base 49, because
- 10 times m-reduction [i] would yield (36, 38, large)-net in base 49, but