Best Known (66, 95, s)-Nets in Base 32
(66, 95, 2343)-Net over F32 — Constructive and digital
Digital (66, 95, 2343)-net over F32, using
- 321 times duplication [i] based on digital (65, 94, 2343)-net over F32, using
- net defined by OOA [i] based on linear OOA(3294, 2343, F32, 29, 29) (dual of [(2343, 29), 67853, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(3294, 32803, F32, 29) (dual of [32803, 32709, 30]-code), using
- construction XX applied to C([0,14]) ⊂ C([0,10]) ⊂ C([0,9]) [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(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(3255, 32769, F32, 19) (dual of [32769, 32714, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(327, 32, F32, 7) (dual of [32, 25, 8]-code or 32-arc in PG(6,32)), using
- Reed–Solomon code RS(25,32) [i]
- linear OA(321, 2, F32, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to C([0,14]) ⊂ C([0,10]) ⊂ C([0,9]) [i] based on
- OOA 14-folding and stacking with additional row [i] based on linear OA(3294, 32803, F32, 29) (dual of [32803, 32709, 30]-code), using
- net defined by OOA [i] based on linear OOA(3294, 2343, F32, 29, 29) (dual of [(2343, 29), 67853, 30]-NRT-code), using
(66, 95, 4681)-Net in Base 32 — Constructive
(66, 95, 4681)-net in base 32, using
- 323 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
(66, 95, 46616)-Net over F32 — Digital
Digital (66, 95, 46616)-net over F32, using
(66, 95, large)-Net in Base 32 — Upper bound on s
There is no (66, 95, large)-net in base 32, because
- 27 times m-reduction [i] would yield (66, 68, large)-net in base 32, but