Best Known (64, 64+30, s)-Nets in Base 32
(64, 64+30, 2186)-Net over F32 — Constructive and digital
Digital (64, 94, 2186)-net over F32, using
- 321 times duplication [i] based on digital (63, 93, 2186)-net over F32, using
- net defined by OOA [i] based on linear OOA(3293, 2186, F32, 30, 30) (dual of [(2186, 30), 65487, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(3293, 32790, F32, 30) (dual of [32790, 32697, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3293, 32791, F32, 30) (dual of [32791, 32698, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(23) [i] based on
- 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(3270, 32768, F32, 24) (dual of [32768, 32698, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(325, 23, F32, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,32)), using
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- Reed–Solomon code RS(27,32) [i]
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- construction X applied to Ce(29) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(3293, 32791, F32, 30) (dual of [32791, 32698, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(3293, 32790, F32, 30) (dual of [32790, 32697, 31]-code), using
- net defined by OOA [i] based on linear OOA(3293, 2186, F32, 30, 30) (dual of [(2186, 30), 65487, 31]-NRT-code), using
(64, 64+30, 32795)-Net over F32 — Digital
Digital (64, 94, 32795)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3294, 32795, F32, 30) (dual of [32795, 32701, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(22) [i] based on
- 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(3267, 32768, F32, 23) (dual of [32768, 32701, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(326, 27, F32, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,32)), using
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
- Reed–Solomon code RS(26,32) [i]
- discarding factors / shortening the dual code based on linear OA(326, 32, F32, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
- construction X applied to Ce(29) ⊂ Ce(22) [i] based on
(64, 64+30, large)-Net in Base 32 — Upper bound on s
There is no (64, 94, large)-net in base 32, because
- 28 times m-reduction [i] would yield (64, 66, large)-net in base 32, but