Best Known (63, 63+30, s)-Nets in Base 32
(63, 63+30, 2186)-Net over F32 — Constructive and digital
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
(63, 63+30, 32133)-Net over F32 — Digital
Digital (63, 93, 32133)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3293, 32133, F32, 30) (dual of [32133, 32040, 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
(63, 63+30, large)-Net in Base 32 — Upper bound on s
There is no (63, 93, large)-net in base 32, because
- 28 times m-reduction [i] would yield (63, 65, large)-net in base 32, but