Best Known (95−32, 95, s)-Nets in Base 32
(95−32, 95, 2048)-Net over F32 — Constructive and digital
Digital (63, 95, 2048)-net over F32, using
- t-expansion [i] based on digital (62, 95, 2048)-net over F32, using
- net defined by OOA [i] based on linear OOA(3295, 2048, F32, 33, 33) (dual of [(2048, 33), 67489, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(3295, 32769, F32, 33) (dual of [32769, 32674, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(3295, 32772, F32, 33) (dual of [32772, 32677, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(30) [i] based on
- linear OA(3294, 32768, F32, 33) (dual of [32768, 32674, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3291, 32768, F32, 31) (dual of [32768, 32677, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(321, 4, F32, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(32) ⊂ Ce(30) [i] based on
- discarding factors / shortening the dual code based on linear OA(3295, 32772, F32, 33) (dual of [32772, 32677, 34]-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(3295, 32769, F32, 33) (dual of [32769, 32674, 34]-code), using
- net defined by OOA [i] based on linear OOA(3295, 2048, F32, 33, 33) (dual of [(2048, 33), 67489, 34]-NRT-code), using
(95−32, 95, 20195)-Net over F32 — Digital
Digital (63, 95, 20195)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3295, 20195, F32, 32) (dual of [20195, 20100, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3295, 32775, F32, 32) (dual of [32775, 32680, 33]-code), using
- 1 times truncation [i] based on linear OA(3296, 32776, F32, 33) (dual of [32776, 32680, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(29) [i] based on
- linear OA(3294, 32768, F32, 33) (dual of [32768, 32674, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3288, 32768, F32, 30) (dual of [32768, 32680, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(322, 8, F32, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- construction X applied to Ce(32) ⊂ Ce(29) [i] based on
- 1 times truncation [i] based on linear OA(3296, 32776, F32, 33) (dual of [32776, 32680, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(3295, 32775, F32, 32) (dual of [32775, 32680, 33]-code), using
(95−32, 95, large)-Net in Base 32 — Upper bound on s
There is no (63, 95, large)-net in base 32, because
- 30 times m-reduction [i] would yield (63, 65, large)-net in base 32, but