Best Known (47, 62, s)-Nets in Base 32
(47, 62, 149800)-Net over F32 — Constructive and digital
Digital (47, 62, 149800)-net over F32, using
- net defined by OOA [i] based on linear OOA(3262, 149800, F32, 15, 15) (dual of [(149800, 15), 2246938, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3262, 1048601, F32, 15) (dual of [1048601, 1048539, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3262, 1048606, F32, 15) (dual of [1048606, 1048544, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,4]) [i] based on
- linear OA(3257, 1048577, F32, 15) (dual of [1048577, 1048520, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(3233, 1048577, F32, 9) (dual of [1048577, 1048544, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(325, 29, F32, 5) (dual of [29, 24, 6]-code or 29-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([0,7]) ⊂ C([0,4]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3262, 1048606, F32, 15) (dual of [1048606, 1048544, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3262, 1048601, F32, 15) (dual of [1048601, 1048539, 16]-code), using
(47, 62, 299594)-Net in Base 32 — Constructive
(47, 62, 299594)-net in base 32, using
- net defined by OOA [i] based on OOA(3262, 299594, S32, 15, 15), using
- OOA 7-folding and stacking with additional row [i] based on OA(3262, 2097159, S32, 15), using
- discarding factors based on OA(3262, 2097160, S32, 15), using
- discarding parts of the base [i] based on linear OA(12844, 2097160, F128, 15) (dual of [2097160, 2097116, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(12843, 2097153, F128, 15) (dual of [2097153, 2097110, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(12837, 2097153, F128, 13) (dual of [2097153, 2097116, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- discarding parts of the base [i] based on linear OA(12844, 2097160, F128, 15) (dual of [2097160, 2097116, 16]-code), using
- discarding factors based on OA(3262, 2097160, S32, 15), using
- OOA 7-folding and stacking with additional row [i] based on OA(3262, 2097159, S32, 15), using
(47, 62, 1048606)-Net over F32 — Digital
Digital (47, 62, 1048606)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3262, 1048606, F32, 15) (dual of [1048606, 1048544, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,4]) [i] based on
- linear OA(3257, 1048577, F32, 15) (dual of [1048577, 1048520, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(3233, 1048577, F32, 9) (dual of [1048577, 1048544, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(325, 29, F32, 5) (dual of [29, 24, 6]-code or 29-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([0,7]) ⊂ C([0,4]) [i] based on
(47, 62, large)-Net in Base 32 — Upper bound on s
There is no (47, 62, large)-net in base 32, because
- 13 times m-reduction [i] would yield (47, 49, large)-net in base 32, but