Best Known (46, 66, s)-Nets in Base 32
(46, 66, 3280)-Net over F32 — Constructive and digital
Digital (46, 66, 3280)-net over F32, using
- net defined by OOA [i] based on linear OOA(3266, 3280, F32, 20, 20) (dual of [(3280, 20), 65534, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3266, 32800, F32, 20) (dual of [32800, 32734, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3266, 32801, F32, 20) (dual of [32801, 32735, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(10) [i] based on
- linear OA(3258, 32768, F32, 20) (dual of [32768, 32710, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- 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(328, 33, F32, 8) (dual of [33, 25, 9]-code or 33-arc in PG(7,32)), using
- extended Reed–Solomon code RSe(25,32) [i]
- construction X applied to Ce(19) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(3266, 32801, F32, 20) (dual of [32801, 32735, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(3266, 32800, F32, 20) (dual of [32800, 32734, 21]-code), using
(46, 66, 6554)-Net in Base 32 — Constructive
(46, 66, 6554)-net in base 32, using
- 322 times duplication [i] based on (44, 64, 6554)-net in base 32, using
- base change [i] based on digital (20, 40, 6554)-net over F256, using
- net defined by OOA [i] based on linear OOA(25640, 6554, F256, 20, 20) (dual of [(6554, 20), 131040, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(25640, 65540, F256, 20) (dual of [65540, 65500, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(25640, 65541, F256, 20) (dual of [65541, 65501, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(25640, 65541, F256, 20) (dual of [65541, 65501, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(25640, 65540, F256, 20) (dual of [65540, 65500, 21]-code), using
- net defined by OOA [i] based on linear OOA(25640, 6554, F256, 20, 20) (dual of [(6554, 20), 131040, 21]-NRT-code), using
- base change [i] based on digital (20, 40, 6554)-net over F256, using
(46, 66, 43288)-Net over F32 — Digital
Digital (46, 66, 43288)-net over F32, using
(46, 66, large)-Net in Base 32 — Upper bound on s
There is no (46, 66, large)-net in base 32, because
- 18 times m-reduction [i] would yield (46, 48, large)-net in base 32, but