Best Known (16, 16+7, s)-Nets in Base 32
(16, 16+7, 11948)-Net over F32 — Constructive and digital
Digital (16, 23, 11948)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 4, 1025)-net over F32, using
- net defined by OOA [i] based on linear OOA(324, 1025, F32, 3, 3) (dual of [(1025, 3), 3071, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(324, 1025, F32, 2, 3) (dual of [(1025, 2), 2046, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(324, 1025, F32, 3, 3) (dual of [(1025, 3), 3071, 4]-NRT-code), using
- digital (12, 19, 10923)-net over F32, using
- net defined by OOA [i] based on linear OOA(3219, 10923, F32, 7, 7) (dual of [(10923, 7), 76442, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(3219, 32770, F32, 7) (dual of [32770, 32751, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(3219, 32771, F32, 7) (dual of [32771, 32752, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(3219, 32768, F32, 7) (dual of [32768, 32749, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(3216, 32768, F32, 6) (dual of [32768, 32752, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 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(3219, 32771, F32, 7) (dual of [32771, 32752, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(3219, 32770, F32, 7) (dual of [32770, 32751, 8]-code), using
- net defined by OOA [i] based on linear OOA(3219, 10923, F32, 7, 7) (dual of [(10923, 7), 76442, 8]-NRT-code), using
- digital (1, 4, 1025)-net over F32, using
(16, 16+7, 56836)-Net over F32 — Digital
Digital (16, 23, 56836)-net over F32, using
(16, 16+7, 87382)-Net in Base 32 — Constructive
(16, 23, 87382)-net in base 32, using
- net defined by OOA [i] based on OOA(3223, 87382, S32, 7, 7), using
- OOA 3-folding and stacking with additional row [i] based on OA(3223, 262147, S32, 7), using
- discarding parts of the base [i] based on linear OA(6419, 262147, F64, 7) (dual of [262147, 262128, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(6419, 262144, F64, 7) (dual of [262144, 262125, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(6416, 262144, F64, 6) (dual of [262144, 262128, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- discarding parts of the base [i] based on linear OA(6419, 262147, F64, 7) (dual of [262147, 262128, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on OA(3223, 262147, S32, 7), using
(16, 16+7, large)-Net in Base 32 — Upper bound on s
There is no (16, 23, large)-net in base 32, because
- 5 times m-reduction [i] would yield (16, 18, large)-net in base 32, but