Best Known (70−23, 70, s)-Nets in Base 32
(70−23, 70, 2980)-Net over F32 — Constructive and digital
Digital (47, 70, 2980)-net over F32, using
- net defined by OOA [i] based on linear OOA(3270, 2980, F32, 23, 23) (dual of [(2980, 23), 68470, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3270, 32781, F32, 23) (dual of [32781, 32711, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3270, 32784, F32, 23) (dual of [32784, 32714, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
- linear OA(3267, 32769, F32, 23) (dual of [32769, 32702, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(3255, 32769, F32, 19) (dual of [32769, 32714, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(323, 15, F32, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,32) or 15-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3270, 32784, F32, 23) (dual of [32784, 32714, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3270, 32781, F32, 23) (dual of [32781, 32711, 24]-code), using
(70−23, 70, 24686)-Net over F32 — Digital
Digital (47, 70, 24686)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3270, 24686, F32, 23) (dual of [24686, 24616, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3270, 32784, F32, 23) (dual of [32784, 32714, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
- linear OA(3267, 32769, F32, 23) (dual of [32769, 32702, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(3255, 32769, F32, 19) (dual of [32769, 32714, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(323, 15, F32, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,32) or 15-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3270, 32784, F32, 23) (dual of [32784, 32714, 24]-code), using
(70−23, 70, large)-Net in Base 32 — Upper bound on s
There is no (47, 70, large)-net in base 32, because
- 21 times m-reduction [i] would yield (47, 49, large)-net in base 32, but