Best Known (71, 71+14, s)-Nets in Base 32
(71, 71+14, 1209294)-Net over F32 — Constructive and digital
Digital (71, 85, 1209294)-net over F32, using
- (u, u+v)-construction [i] based on
- 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 (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 (12, 19, 10923)-net over F32, using
(71, 71+14, 1220216)-Net in Base 32 — Constructive
(71, 85, 1220216)-net in base 32, using
- (u, u+v)-construction [i] based on
- (14, 21, 21845)-net in base 32, using
- net defined by OOA [i] based on OOA(3221, 21845, S32, 7, 7), using
- OOA 3-folding and stacking with additional row [i] based on OA(3221, 65536, S32, 7), using
- discarding factors based on OA(3221, 65538, S32, 7), using
- discarding parts of the base [i] based on linear OA(25613, 65538, F256, 7) (dual of [65538, 65525, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(25613, 65536, F256, 7) (dual of [65536, 65523, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 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(25613, 65538, F256, 7) (dual of [65538, 65525, 8]-code), using
- discarding factors based on OA(3221, 65538, S32, 7), using
- OOA 3-folding and stacking with additional row [i] based on OA(3221, 65536, S32, 7), using
- net defined by OOA [i] based on OOA(3221, 21845, S32, 7, 7), using
- (50, 64, 1198371)-net in base 32, using
- base change [i] based on digital (26, 40, 1198371)-net over F256, using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- base change [i] based on digital (26, 40, 1198371)-net over F256, using
- (14, 21, 21845)-net in base 32, using
(71, 71+14, large)-Net over F32 — Digital
Digital (71, 85, large)-net over F32, using
- t-expansion [i] based on digital (68, 85, large)-net over F32, using
- 1 times m-reduction [i] based on digital (68, 86, large)-net over F32, using
(71, 71+14, large)-Net in Base 32 — Upper bound on s
There is no (71, 85, large)-net in base 32, because
- 12 times m-reduction [i] would yield (71, 73, large)-net in base 32, but