Best Known (96−14, 96, s)-Nets in Base 32
(96−14, 96, 1551033)-Net over F32 — Constructive and digital
Digital (82, 96, 1551033)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (23, 30, 352662)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (2, 5, 3136)-net over F32, using
- net defined by OOA [i] based on linear OOA(325, 3136, F32, 3, 3) (dual of [(3136, 3), 9403, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(325, 3136, F32, 2, 3) (dual of [(3136, 2), 6267, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(325, 3136, F32, 3, 3) (dual of [(3136, 3), 9403, 4]-NRT-code), using
- digital (18, 25, 349526)-net over F32, using
- net defined by OOA [i] based on linear OOA(3225, 349526, F32, 7, 7) (dual of [(349526, 7), 2446657, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(3225, 1048579, F32, 7) (dual of [1048579, 1048554, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(3225, 1048580, F32, 7) (dual of [1048580, 1048555, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(3225, 1048576, F32, 7) (dual of [1048576, 1048551, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(3221, 1048576, F32, 6) (dual of [1048576, 1048555, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(3225, 1048580, F32, 7) (dual of [1048580, 1048555, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(3225, 1048579, F32, 7) (dual of [1048579, 1048554, 8]-code), using
- net defined by OOA [i] based on linear OOA(3225, 349526, F32, 7, 7) (dual of [(349526, 7), 2446657, 8]-NRT-code), using
- digital (2, 5, 3136)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (52, 66, 1198371)-net over F32, using
- net defined by OOA [i] based on linear OOA(3266, 1198371, F32, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3266, 8388597, F32, 14) (dual of [8388597, 8388531, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3266, large, F32, 14) (dual of [large, large−66, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(3266, large, F32, 14) (dual of [large, large−66, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3266, 8388597, F32, 14) (dual of [8388597, 8388531, 15]-code), using
- net defined by OOA [i] based on linear OOA(3266, 1198371, F32, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- digital (23, 30, 352662)-net over F32, using
(96−14, 96, 2396742)-Net in Base 32 — Constructive
(82, 96, 2396742)-net in base 32, using
- base change [i] based on digital (66, 80, 2396742)-net over F64, using
- 642 times duplication [i] based on digital (64, 78, 2396742)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (18, 25, 2796200)-net over F64, using
- net defined by OOA [i] based on linear OOA(6425, 2796200, F64, 7, 7) (dual of [(2796200, 7), 19573375, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(6425, 8388601, F64, 7) (dual of [8388601, 8388576, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(6425, large, F64, 7) (dual of [large, large−25, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6425, large, F64, 7) (dual of [large, large−25, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(6425, 8388601, F64, 7) (dual of [8388601, 8388576, 8]-code), using
- net defined by OOA [i] based on linear OOA(6425, 2796200, F64, 7, 7) (dual of [(2796200, 7), 19573375, 8]-NRT-code), using
- digital (39, 53, 1198371)-net over F64, using
- net defined by OOA [i] based on linear OOA(6453, 1198371, F64, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(6453, 8388597, F64, 14) (dual of [8388597, 8388544, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(6453, large, F64, 14) (dual of [large, large−53, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(6453, large, F64, 14) (dual of [large, large−53, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(6453, 8388597, F64, 14) (dual of [8388597, 8388544, 15]-code), using
- net defined by OOA [i] based on linear OOA(6453, 1198371, F64, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
- digital (18, 25, 2796200)-net over F64, using
- (u, u+v)-construction [i] based on
- 642 times duplication [i] based on digital (64, 78, 2396742)-net over F64, using
(96−14, 96, large)-Net over F32 — Digital
Digital (82, 96, large)-net over F32, using
- t-expansion [i] based on digital (79, 96, large)-net over F32, using
- 4 times m-reduction [i] based on digital (79, 100, large)-net over F32, using
(96−14, 96, large)-Net in Base 32 — Upper bound on s
There is no (82, 96, large)-net in base 32, because
- 12 times m-reduction [i] would yield (82, 84, large)-net in base 32, but