Best Known (66, 97, s)-Nets in Base 32
(66, 97, 2186)-Net over F32 — Constructive and digital
Digital (66, 97, 2186)-net over F32, using
- 321 times duplication [i] based on digital (65, 96, 2186)-net over F32, using
- net defined by OOA [i] based on linear OOA(3296, 2186, F32, 31, 31) (dual of [(2186, 31), 67670, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(3296, 32791, F32, 31) (dual of [32791, 32695, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3296, 32792, F32, 31) (dual of [32792, 32696, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,12]) [i] based on
- linear OA(3291, 32769, F32, 31) (dual of [32769, 32678, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(3273, 32769, F32, 25) (dual of [32769, 32696, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [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 C([0,15]) ⊂ C([0,12]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3296, 32792, F32, 31) (dual of [32792, 32696, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(3296, 32791, F32, 31) (dual of [32791, 32695, 32]-code), using
- net defined by OOA [i] based on linear OOA(3296, 2186, F32, 31, 31) (dual of [(2186, 31), 67670, 32]-NRT-code), using
(66, 97, 32795)-Net over F32 — Digital
Digital (66, 97, 32795)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3297, 32795, F32, 31) (dual of [32795, 32698, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(23) [i] based on
- linear OA(3291, 32768, F32, 31) (dual of [32768, 32677, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(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(30) ⊂ Ce(23) [i] based on
(66, 97, large)-Net in Base 32 — Upper bound on s
There is no (66, 97, large)-net in base 32, because
- 29 times m-reduction [i] would yield (66, 68, large)-net in base 32, but