Best Known (45, 65, s)-Nets in Base 32
(45, 65, 3279)-Net over F32 — Constructive and digital
Digital (45, 65, 3279)-net over F32, using
- 1 times m-reduction [i] based on digital (45, 66, 3279)-net over F32, using
- net defined by OOA [i] based on linear OOA(3266, 3279, F32, 21, 21) (dual of [(3279, 21), 68793, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3266, 32791, F32, 21) (dual of [32791, 32725, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3266, 32792, F32, 21) (dual of [32792, 32726, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,7]) [i] based on
- linear OA(3261, 32769, F32, 21) (dual of [32769, 32708, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(3243, 32769, F32, 15) (dual of [32769, 32726, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (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([0,10]) ⊂ C([0,7]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3266, 32792, F32, 21) (dual of [32792, 32726, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3266, 32791, F32, 21) (dual of [32791, 32725, 22]-code), using
- net defined by OOA [i] based on linear OOA(3266, 3279, F32, 21, 21) (dual of [(3279, 21), 68793, 22]-NRT-code), using
(45, 65, 6554)-Net in Base 32 — Constructive
(45, 65, 6554)-net in base 32, using
- 321 times duplication [i] based on (44, 64, 6554)-net in base 32, using
- base change [i] based on digital (20, 40, 6554)-net over F256, using
- net defined by OOA [i] based on linear OOA(25640, 6554, F256, 20, 20) (dual of [(6554, 20), 131040, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(25640, 65540, F256, 20) (dual of [65540, 65500, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(25640, 65541, F256, 20) (dual of [65541, 65501, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(25640, 65541, F256, 20) (dual of [65541, 65501, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(25640, 65540, F256, 20) (dual of [65540, 65500, 21]-code), using
- net defined by OOA [i] based on linear OOA(25640, 6554, F256, 20, 20) (dual of [(6554, 20), 131040, 21]-NRT-code), using
- base change [i] based on digital (20, 40, 6554)-net over F256, using
(45, 65, 36072)-Net over F32 — Digital
Digital (45, 65, 36072)-net over F32, using
(45, 65, large)-Net in Base 32 — Upper bound on s
There is no (45, 65, large)-net in base 32, because
- 18 times m-reduction [i] would yield (45, 47, large)-net in base 32, but