Best Known (60, 88, s)-Nets in Base 32
(60, 88, 2342)-Net over F32 — Constructive and digital
Digital (60, 88, 2342)-net over F32, using
- 321 times duplication [i] based on digital (59, 87, 2342)-net over F32, using
- net defined by OOA [i] based on linear OOA(3287, 2342, F32, 28, 28) (dual of [(2342, 28), 65489, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(3287, 32788, F32, 28) (dual of [32788, 32701, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3287, 32791, F32, 28) (dual of [32791, 32704, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- linear OA(3282, 32768, F32, 28) (dual of [32768, 32686, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3264, 32768, F32, 22) (dual of [32768, 32704, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(27) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(3287, 32791, F32, 28) (dual of [32791, 32704, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(3287, 32788, F32, 28) (dual of [32788, 32701, 29]-code), using
- net defined by OOA [i] based on linear OOA(3287, 2342, F32, 28, 28) (dual of [(2342, 28), 65489, 29]-NRT-code), using
(60, 88, 4681)-Net in Base 32 — Constructive
(60, 88, 4681)-net in base 32, using
- base change [i] based on digital (27, 55, 4681)-net over F256, using
- net defined by OOA [i] based on linear OOA(25655, 4681, F256, 28, 28) (dual of [(4681, 28), 131013, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(25655, 65534, F256, 28) (dual of [65534, 65479, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(25655, 65534, F256, 28) (dual of [65534, 65479, 29]-code), using
- net defined by OOA [i] based on linear OOA(25655, 4681, F256, 28, 28) (dual of [(4681, 28), 131013, 29]-NRT-code), using
(60, 88, 32795)-Net over F32 — Digital
Digital (60, 88, 32795)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3288, 32795, F32, 28) (dual of [32795, 32707, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(20) [i] based on
- linear OA(3282, 32768, F32, 28) (dual of [32768, 32686, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3261, 32768, F32, 21) (dual of [32768, 32707, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(27) ⊂ Ce(20) [i] based on
(60, 88, large)-Net in Base 32 — Upper bound on s
There is no (60, 88, large)-net in base 32, because
- 26 times m-reduction [i] would yield (60, 62, large)-net in base 32, but