Best Known (69, 98, s)-Nets in Base 32
(69, 98, 2343)-Net over F32 — Constructive and digital
Digital (69, 98, 2343)-net over F32, using
- 324 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
(69, 98, 4682)-Net in Base 32 — Constructive
(69, 98, 4682)-net in base 32, using
- 321 times duplication [i] based on (68, 97, 4682)-net in base 32, using
- net defined by OOA [i] based on OOA(3297, 4682, S32, 29, 29), using
- OOA 14-folding and stacking with additional row [i] based on OA(3297, 65549, S32, 29), using
- 1 times code embedding in larger space [i] based on OA(3296, 65548, S32, 29), using
- discarding parts of the base [i] based on linear OA(25660, 65548, F256, 29) (dual of [65548, 65488, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [i] based on
- linear OA(25657, 65537, F256, 29) (dual of [65537, 65480, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(25649, 65537, F256, 25) (dual of [65537, 65488, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [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 C([0,14]) ⊂ C([0,12]) [i] based on
- discarding parts of the base [i] based on linear OA(25660, 65548, F256, 29) (dual of [65548, 65488, 30]-code), using
- 1 times code embedding in larger space [i] based on OA(3296, 65548, S32, 29), using
- OOA 14-folding and stacking with additional row [i] based on OA(3297, 65549, S32, 29), using
- net defined by OOA [i] based on OOA(3297, 4682, S32, 29, 29), using
(69, 98, 67571)-Net over F32 — Digital
Digital (69, 98, 67571)-net over F32, using
(69, 98, large)-Net in Base 32 — Upper bound on s
There is no (69, 98, large)-net in base 32, because
- 27 times m-reduction [i] would yield (69, 71, large)-net in base 32, but