Best Known (67, 67+28, s)-Nets in Base 32
(67, 67+28, 2343)-Net over F32 — Constructive and digital
Digital (67, 95, 2343)-net over F32, using
- 321 times duplication [i] based on digital (66, 94, 2343)-net over F32, using
- t-expansion [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
- t-expansion [i] based on digital (65, 94, 2343)-net over F32, using
(67, 67+28, 4682)-Net in Base 32 — Constructive
(67, 95, 4682)-net in base 32, using
- 321 times duplication [i] based on (66, 94, 4682)-net in base 32, using
- net defined by OOA [i] based on OOA(3294, 4682, S32, 28, 28), using
- OA 14-folding and stacking [i] based on OA(3294, 65548, S32, 28), using
- 1 times code embedding in larger space [i] based on OA(3293, 65547, S32, 28), using
- discarding parts of the base [i] based on linear OA(25658, 65547, F256, 28) (dual of [65547, 65489, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(23) [i] 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]
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2563, 11, F256, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- Reed–Solomon code RS(253,256) [i]
- discarding factors / shortening the dual code based on linear OA(2563, 256, F256, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
- construction X applied to Ce(27) ⊂ Ce(23) [i] based on
- discarding parts of the base [i] based on linear OA(25658, 65547, F256, 28) (dual of [65547, 65489, 29]-code), using
- 1 times code embedding in larger space [i] based on OA(3293, 65547, S32, 28), using
- OA 14-folding and stacking [i] based on OA(3294, 65548, S32, 28), using
- net defined by OOA [i] based on OOA(3294, 4682, S32, 28, 28), using
(67, 67+28, 69667)-Net over F32 — Digital
Digital (67, 95, 69667)-net over F32, using
(67, 67+28, large)-Net in Base 32 — Upper bound on s
There is no (67, 95, large)-net in base 32, because
- 26 times m-reduction [i] would yield (67, 69, large)-net in base 32, but