Best Known (90, 90+19, s)-Nets in Base 32
(90, 90+19, 932323)-Net over F32 — Constructive and digital
Digital (90, 109, 932323)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (9, 18, 257)-net over F32, using
- net defined by OOA [i] based on linear OOA(3218, 257, F32, 9, 9) (dual of [(257, 9), 2295, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3218, 1029, F32, 9) (dual of [1029, 1011, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(3218, 1030, F32, 9) (dual of [1030, 1012, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(3217, 1025, F32, 9) (dual of [1025, 1008, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(3213, 1025, F32, 7) (dual of [1025, 1012, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(321, 5, F32, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3218, 1030, F32, 9) (dual of [1030, 1012, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(3218, 1029, F32, 9) (dual of [1029, 1011, 10]-code), using
- net defined by OOA [i] based on linear OOA(3218, 257, F32, 9, 9) (dual of [(257, 9), 2295, 10]-NRT-code), using
- digital (72, 91, 932066)-net over F32, using
- net defined by OOA [i] based on linear OOA(3291, 932066, F32, 19, 19) (dual of [(932066, 19), 17709163, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3291, 8388595, F32, 19) (dual of [8388595, 8388504, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3291, large, F32, 19) (dual of [large, large−91, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3291, large, F32, 19) (dual of [large, large−91, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3291, 8388595, F32, 19) (dual of [8388595, 8388504, 20]-code), using
- net defined by OOA [i] based on linear OOA(3291, 932066, F32, 19, 19) (dual of [(932066, 19), 17709163, 20]-NRT-code), using
- digital (9, 18, 257)-net over F32, using
(90, 90+19, 933090)-Net in Base 32 — Constructive
(90, 109, 933090)-net in base 32, using
- 321 times duplication [i] based on (89, 108, 933090)-net in base 32, using
- base change [i] based on digital (71, 90, 933090)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (8, 17, 1024)-net over F64, using
- net defined by OOA [i] based on linear OOA(6417, 1024, F64, 9, 9) (dual of [(1024, 9), 9199, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(6417, 4097, F64, 9) (dual of [4097, 4080, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- OOA 4-folding and stacking with additional row [i] based on linear OA(6417, 4097, F64, 9) (dual of [4097, 4080, 10]-code), using
- net defined by OOA [i] based on linear OOA(6417, 1024, F64, 9, 9) (dual of [(1024, 9), 9199, 10]-NRT-code), using
- digital (54, 73, 932066)-net over F64, using
- net defined by OOA [i] based on linear OOA(6473, 932066, F64, 19, 19) (dual of [(932066, 19), 17709181, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(6473, 8388595, F64, 19) (dual of [8388595, 8388522, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(6473, large, F64, 19) (dual of [large, large−73, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6473, large, F64, 19) (dual of [large, large−73, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(6473, 8388595, F64, 19) (dual of [8388595, 8388522, 20]-code), using
- net defined by OOA [i] based on linear OOA(6473, 932066, F64, 19, 19) (dual of [(932066, 19), 17709181, 20]-NRT-code), using
- digital (8, 17, 1024)-net over F64, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (71, 90, 933090)-net over F64, using
(90, 90+19, large)-Net over F32 — Digital
Digital (90, 109, large)-net over F32, using
- t-expansion [i] based on digital (87, 109, large)-net over F32, using
- 1 times m-reduction [i] based on digital (87, 110, large)-net over F32, using
(90, 90+19, large)-Net in Base 32 — Upper bound on s
There is no (90, 109, large)-net in base 32, because
- 17 times m-reduction [i] would yield (90, 92, large)-net in base 32, but