Best Known (67, 100, s)-Nets in Base 32
(67, 100, 2049)-Net over F32 — Constructive and digital
Digital (67, 100, 2049)-net over F32, using
- 321 times duplication [i] based on digital (66, 99, 2049)-net over F32, using
- net defined by OOA [i] based on linear OOA(3299, 2049, F32, 33, 33) (dual of [(2049, 33), 67518, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(3299, 32785, F32, 33) (dual of [32785, 32686, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(3299, 32788, F32, 33) (dual of [32788, 32689, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(26) [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(3279, 32768, F32, 27) (dual of [32768, 32689, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(325, 20, F32, 5) (dual of [20, 15, 6]-code or 20-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(32) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(3299, 32788, F32, 33) (dual of [32788, 32689, 34]-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(3299, 32785, F32, 33) (dual of [32785, 32686, 34]-code), using
- net defined by OOA [i] based on linear OOA(3299, 2049, F32, 33, 33) (dual of [(2049, 33), 67518, 34]-NRT-code), using
(67, 100, 25655)-Net over F32 — Digital
Digital (67, 100, 25655)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(32100, 25655, F32, 33) (dual of [25655, 25555, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(32100, 32784, F32, 33) (dual of [32784, 32684, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [i] based on
- linear OA(3297, 32769, F32, 33) (dual of [32769, 32672, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(3285, 32769, F32, 29) (dual of [32769, 32684, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(323, 15, F32, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,32) or 15-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 C([0,16]) ⊂ C([0,14]) [i] based on
- discarding factors / shortening the dual code based on linear OA(32100, 32784, F32, 33) (dual of [32784, 32684, 34]-code), using
(67, 100, large)-Net in Base 32 — Upper bound on s
There is no (67, 100, large)-net in base 32, because
- 31 times m-reduction [i] would yield (67, 69, large)-net in base 32, but