Best Known (67, 67+22, s)-Nets in Base 32
(67, 67+22, 95327)-Net over F32 — Constructive and digital
Digital (67, 89, 95327)-net over F32, using
- net defined by OOA [i] based on linear OOA(3289, 95327, F32, 22, 22) (dual of [(95327, 22), 2097105, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3289, 1048597, F32, 22) (dual of [1048597, 1048508, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3289, 1048600, F32, 22) (dual of [1048600, 1048511, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(3285, 1048576, F32, 22) (dual of [1048576, 1048491, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3265, 1048576, F32, 17) (dual of [1048576, 1048511, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(324, 24, F32, 4) (dual of [24, 20, 5]-code or 24-arc in PG(3,32)), using
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- Reed–Solomon code RS(28,32) [i]
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(3289, 1048600, F32, 22) (dual of [1048600, 1048511, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3289, 1048597, F32, 22) (dual of [1048597, 1048508, 23]-code), using
(67, 67+22, 1048600)-Net over F32 — Digital
Digital (67, 89, 1048600)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3289, 1048600, F32, 22) (dual of [1048600, 1048511, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(3285, 1048576, F32, 22) (dual of [1048576, 1048491, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3265, 1048576, F32, 17) (dual of [1048576, 1048511, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(324, 24, F32, 4) (dual of [24, 20, 5]-code or 24-arc in PG(3,32)), using
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- Reed–Solomon code RS(28,32) [i]
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
(67, 67+22, large)-Net in Base 32 — Upper bound on s
There is no (67, 89, large)-net in base 32, because
- 20 times m-reduction [i] would yield (67, 69, large)-net in base 32, but