Best Known (48−11, 48, s)-Nets in Base 32
(48−11, 48, 210211)-Net over F32 — Constructive and digital
Digital (37, 48, 210211)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 496)-net over F32, using
- net defined by OOA [i] based on linear OOA(327, 496, F32, 5, 5) (dual of [(496, 5), 2473, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(327, 993, F32, 5) (dual of [993, 986, 6]-code), using
- net defined by OOA [i] based on linear OOA(327, 496, F32, 5, 5) (dual of [(496, 5), 2473, 6]-NRT-code), using
- digital (30, 41, 209715)-net over F32, using
- net defined by OOA [i] based on linear OOA(3241, 209715, F32, 11, 11) (dual of [(209715, 11), 2306824, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(3241, 1048576, F32, 11) (dual of [1048576, 1048535, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(3241, 1048576, F32, 11) (dual of [1048576, 1048535, 12]-code), using
- net defined by OOA [i] based on linear OOA(3241, 209715, F32, 11, 11) (dual of [(209715, 11), 2306824, 12]-NRT-code), using
- digital (2, 7, 496)-net over F32, using
(48−11, 48, 419433)-Net in Base 32 — Constructive
(37, 48, 419433)-net in base 32, using
- net defined by OOA [i] based on OOA(3248, 419433, S32, 11, 11), using
- OOA 5-folding and stacking with additional row [i] based on OA(3248, 2097166, S32, 11), using
- discarding factors based on OA(3248, 2097168, S32, 11), using
- discarding parts of the base [i] based on linear OA(12834, 2097168, F128, 11) (dual of [2097168, 2097134, 12]-code), using
- construction X applied to C([0,5]) ⊂ C([0,3]) [i] based on
- linear OA(12831, 2097153, F128, 11) (dual of [2097153, 2097122, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(12819, 2097153, F128, 7) (dual of [2097153, 2097134, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(1283, 15, F128, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,128) or 15-cap in PG(2,128)), using
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- Reed–Solomon code RS(125,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- construction X applied to C([0,5]) ⊂ C([0,3]) [i] based on
- discarding parts of the base [i] based on linear OA(12834, 2097168, F128, 11) (dual of [2097168, 2097134, 12]-code), using
- discarding factors based on OA(3248, 2097168, S32, 11), using
- OOA 5-folding and stacking with additional row [i] based on OA(3248, 2097166, S32, 11), using
(48−11, 48, 2450955)-Net over F32 — Digital
Digital (37, 48, 2450955)-net over F32, using
(48−11, 48, large)-Net in Base 32 — Upper bound on s
There is no (37, 48, large)-net in base 32, because
- 9 times m-reduction [i] would yield (37, 39, large)-net in base 32, but