Best Known (48, 48+15, s)-Nets in Base 32
(48, 48+15, 149801)-Net over F32 — Constructive and digital
Digital (48, 63, 149801)-net over F32, using
- net defined by OOA [i] based on linear OOA(3263, 149801, F32, 15, 15) (dual of [(149801, 15), 2246952, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3263, 1048608, F32, 15) (dual of [1048608, 1048545, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3263, 1048609, F32, 15) (dual of [1048609, 1048546, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(7) [i] based on
- linear OA(3257, 1048576, F32, 15) (dual of [1048576, 1048519, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(3229, 1048576, F32, 8) (dual of [1048576, 1048547, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(326, 33, F32, 6) (dual of [33, 27, 7]-code or 33-arc in PG(5,32)), using
- extended Reed–Solomon code RSe(27,32) [i]
- construction X applied to Ce(14) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(3263, 1048609, F32, 15) (dual of [1048609, 1048546, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3263, 1048608, F32, 15) (dual of [1048608, 1048545, 16]-code), using
(48, 48+15, 299594)-Net in Base 32 — Constructive
(48, 63, 299594)-net in base 32, using
- base change [i] based on digital (30, 45, 299594)-net over F128, using
- 1281 times duplication [i] based on digital (29, 44, 299594)-net over F128, using
- net defined by OOA [i] based on linear OOA(12844, 299594, F128, 15, 15) (dual of [(299594, 15), 4493866, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(12844, 2097159, F128, 15) (dual of [2097159, 2097115, 16]-code), using
- discarding factors / shortening the dual code 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 factors / shortening the dual code based on linear OA(12844, 2097160, F128, 15) (dual of [2097160, 2097116, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(12844, 2097159, F128, 15) (dual of [2097159, 2097115, 16]-code), using
- net defined by OOA [i] based on linear OOA(12844, 299594, F128, 15, 15) (dual of [(299594, 15), 4493866, 16]-NRT-code), using
- 1281 times duplication [i] based on digital (29, 44, 299594)-net over F128, using
(48, 48+15, 1156841)-Net over F32 — Digital
Digital (48, 63, 1156841)-net over F32, using
(48, 48+15, large)-Net in Base 32 — Upper bound on s
There is no (48, 63, large)-net in base 32, because
- 13 times m-reduction [i] would yield (48, 50, large)-net in base 32, but