Best Known (93−29, 93, s)-Nets in Base 32
(93−29, 93, 2342)-Net over F32 — Constructive and digital
Digital (64, 93, 2342)-net over F32, using
- 323 times duplication [i] based on digital (61, 90, 2342)-net over F32, using
- net defined by OOA [i] based on linear OOA(3290, 2342, F32, 29, 29) (dual of [(2342, 29), 67828, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(3290, 32789, F32, 29) (dual of [32789, 32699, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(3290, 32792, F32, 29) (dual of [32792, 32702, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,11]) [i] based on
- 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(3267, 32769, F32, 23) (dual of [32769, 32702, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (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([0,14]) ⊂ C([0,11]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3290, 32792, F32, 29) (dual of [32792, 32702, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(3290, 32789, F32, 29) (dual of [32789, 32699, 30]-code), using
- net defined by OOA [i] based on linear OOA(3290, 2342, F32, 29, 29) (dual of [(2342, 29), 67828, 30]-NRT-code), using
(93−29, 93, 4681)-Net in Base 32 — Constructive
(64, 93, 4681)-net in base 32, using
- 321 times duplication [i] based on (63, 92, 4681)-net in base 32, using
- net defined by OOA [i] based on OOA(3292, 4681, S32, 29, 29), using
- OOA 14-folding and stacking with additional row [i] based on OA(3292, 65535, S32, 29), using
- discarding factors based on OA(3292, 65538, S32, 29), using
- discarding parts of the base [i] based on linear OA(25657, 65538, F256, 29) (dual of [65538, 65481, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(25657, 65536, F256, 29) (dual of [65536, 65479, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- 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]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- discarding parts of the base [i] based on linear OA(25657, 65538, F256, 29) (dual of [65538, 65481, 30]-code), using
- discarding factors based on OA(3292, 65538, S32, 29), using
- OOA 14-folding and stacking with additional row [i] based on OA(3292, 65535, S32, 29), using
- net defined by OOA [i] based on OOA(3292, 4681, S32, 29, 29), using
(93−29, 93, 36396)-Net over F32 — Digital
Digital (64, 93, 36396)-net over F32, using
(93−29, 93, large)-Net in Base 32 — Upper bound on s
There is no (64, 93, large)-net in base 32, because
- 27 times m-reduction [i] would yield (64, 66, large)-net in base 32, but