Best Known (66, 66+22, s)-Nets in Base 32
(66, 66+22, 95326)-Net over F32 — Constructive and digital
Digital (66, 88, 95326)-net over F32, using
- 321 times duplication [i] based on digital (65, 87, 95326)-net over F32, using
- net defined by OOA [i] based on linear OOA(3287, 95326, F32, 22, 22) (dual of [(95326, 22), 2097085, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3287, 1048586, F32, 22) (dual of [1048586, 1048499, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3287, 1048590, F32, 22) (dual of [1048590, 1048503, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [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(3273, 1048576, F32, 19) (dual of [1048576, 1048503, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(322, 14, F32, 2) (dual of [14, 12, 3]-code or 14-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(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(3287, 1048590, F32, 22) (dual of [1048590, 1048503, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3287, 1048586, F32, 22) (dual of [1048586, 1048499, 23]-code), using
- net defined by OOA [i] based on linear OOA(3287, 95326, F32, 22, 22) (dual of [(95326, 22), 2097085, 23]-NRT-code), using
(66, 66+22, 944806)-Net over F32 — Digital
Digital (66, 88, 944806)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3288, 944806, F32, 22) (dual of [944806, 944718, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3288, 1048595, F32, 22) (dual of [1048595, 1048507, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [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(3269, 1048576, F32, 18) (dual of [1048576, 1048507, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(323, 19, F32, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,32) or 19-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(21) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(3288, 1048595, F32, 22) (dual of [1048595, 1048507, 23]-code), using
(66, 66+22, large)-Net in Base 32 — Upper bound on s
There is no (66, 88, large)-net in base 32, because
- 20 times m-reduction [i] would yield (66, 68, large)-net in base 32, but