Best Known (32−8, 32, s)-Nets in Base 49
(32−8, 32, 1441205)-Net over F49 — Constructive and digital
Digital (24, 32, 1441205)-net over F49, using
- net defined by OOA [i] based on linear OOA(4932, 1441205, F49, 8, 8) (dual of [(1441205, 8), 11529608, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(4932, 5764820, F49, 8) (dual of [5764820, 5764788, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(3) [i] based on
- 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(4913, 5764801, F49, 4) (dual of [5764801, 5764788, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(7) ⊂ Ce(3) [i] based on
- OA 4-folding and stacking [i] based on linear OA(4932, 5764820, F49, 8) (dual of [5764820, 5764788, 9]-code), using
(32−8, 32, 5764820)-Net over F49 — Digital
Digital (24, 32, 5764820)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4932, 5764820, F49, 8) (dual of [5764820, 5764788, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(3) [i] based on
- 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(4913, 5764801, F49, 4) (dual of [5764801, 5764788, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(7) ⊂ Ce(3) [i] based on
(32−8, 32, large)-Net in Base 49 — Upper bound on s
There is no (24, 32, large)-net in base 49, because
- 6 times m-reduction [i] would yield (24, 26, large)-net in base 49, but