Best Known (96−32, 96, s)-Nets in Base 32
(96−32, 96, 2048)-Net over F32 — Constructive and digital
Digital (64, 96, 2048)-net over F32, using
- 321 times duplication [i] based on 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
- t-expansion [i] based on digital (62, 95, 2048)-net over F32, using
(96−32, 96, 22670)-Net over F32 — Digital
Digital (64, 96, 22670)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3296, 22670, F32, 32) (dual of [22670, 22574, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3296, 32779, F32, 32) (dual of [32779, 32683, 33]-code), using
- 1 times truncation [i] based on linear OA(3297, 32780, F32, 33) (dual of [32780, 32683, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(28) [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(3285, 32768, F32, 29) (dual of [32768, 32683, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(323, 12, F32, 3) (dual of [12, 9, 4]-code or 12-arc in PG(2,32) or 12-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 Ce(32) ⊂ Ce(28) [i] based on
- 1 times truncation [i] based on linear OA(3297, 32780, F32, 33) (dual of [32780, 32683, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(3296, 32779, F32, 32) (dual of [32779, 32683, 33]-code), using
(96−32, 96, large)-Net in Base 32 — Upper bound on s
There is no (64, 96, large)-net in base 32, because
- 30 times m-reduction [i] would yield (64, 66, large)-net in base 32, but