Best Known (27, 38, s)-Nets in Base 32
(27, 38, 7050)-Net over F32 — Constructive and digital
Digital (27, 38, 7050)-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 (20, 31, 6554)-net over F32, using
- net defined by OOA [i] based on linear OOA(3231, 6554, F32, 11, 11) (dual of [(6554, 11), 72063, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(3231, 32771, F32, 11) (dual of [32771, 32740, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(3231, 32768, F32, 11) (dual of [32768, 32737, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(3228, 32768, F32, 10) (dual of [32768, 32740, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(10) ⊂ Ce(9) [i] based on
- OOA 5-folding and stacking with additional row [i] based on linear OA(3231, 32771, F32, 11) (dual of [32771, 32740, 12]-code), using
- net defined by OOA [i] based on linear OOA(3231, 6554, F32, 11, 11) (dual of [(6554, 11), 72063, 12]-NRT-code), using
- digital (2, 7, 496)-net over F32, using
(27, 38, 52429)-Net in Base 32 — Constructive
(27, 38, 52429)-net in base 32, using
- net defined by OOA [i] based on OOA(3238, 52429, S32, 11, 11), using
- OOA 5-folding and stacking with additional row [i] based on OA(3238, 262146, S32, 11), using
- discarding factors based on OA(3238, 262147, S32, 11), using
- discarding parts of the base [i] based on linear OA(6431, 262147, F64, 11) (dual of [262147, 262116, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(6431, 262144, F64, 11) (dual of [262144, 262113, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(6428, 262144, F64, 10) (dual of [262144, 262116, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(10) ⊂ Ce(9) [i] based on
- discarding parts of the base [i] based on linear OA(6431, 262147, F64, 11) (dual of [262147, 262116, 12]-code), using
- discarding factors based on OA(3238, 262147, S32, 11), using
- OOA 5-folding and stacking with additional row [i] based on OA(3238, 262146, S32, 11), using
(27, 38, 76597)-Net over F32 — Digital
Digital (27, 38, 76597)-net over F32, using
(27, 38, large)-Net in Base 32 — Upper bound on s
There is no (27, 38, large)-net in base 32, because
- 9 times m-reduction [i] would yield (27, 29, large)-net in base 32, but