Best Known (28, 42, s)-Nets in Base 32
(28, 42, 4682)-Net over F32 — Constructive and digital
Digital (28, 42, 4682)-net over F32, using
- 321 times duplication [i] based on digital (27, 41, 4682)-net over F32, using
- net defined by OOA [i] based on linear OOA(3241, 4682, F32, 14, 14) (dual of [(4682, 14), 65507, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3241, 32774, F32, 14) (dual of [32774, 32733, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3241, 32775, F32, 14) (dual of [32775, 32734, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(3240, 32768, F32, 14) (dual of [32768, 32728, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(3234, 32768, F32, 12) (dual of [32768, 32734, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(321, 7, F32, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(3241, 32775, F32, 14) (dual of [32775, 32734, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3241, 32774, F32, 14) (dual of [32774, 32733, 15]-code), using
- net defined by OOA [i] based on linear OOA(3241, 4682, F32, 14, 14) (dual of [(4682, 14), 65507, 15]-NRT-code), using
(28, 42, 23686)-Net over F32 — Digital
Digital (28, 42, 23686)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3242, 23686, F32, 14) (dual of [23686, 23644, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3242, 32779, F32, 14) (dual of [32779, 32737, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(3240, 32768, F32, 14) (dual of [32768, 32728, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(322, 11, F32, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(3242, 32779, F32, 14) (dual of [32779, 32737, 15]-code), using
(28, 42, large)-Net in Base 32 — Upper bound on s
There is no (28, 42, large)-net in base 32, because
- 12 times m-reduction [i] would yield (28, 30, large)-net in base 32, but