Best Known (83−28, 83, s)-Nets in Base 32
(83−28, 83, 2341)-Net over F32 — Constructive and digital
Digital (55, 83, 2341)-net over F32, using
- net defined by OOA [i] based on linear OOA(3283, 2341, F32, 28, 28) (dual of [(2341, 28), 65465, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(3283, 32774, F32, 28) (dual of [32774, 32691, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3283, 32775, F32, 28) (dual of [32775, 32692, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(3282, 32768, F32, 28) (dual of [32768, 32686, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3276, 32768, F32, 26) (dual of [32768, 32692, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3283, 32775, F32, 28) (dual of [32775, 32692, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(3283, 32774, F32, 28) (dual of [32774, 32691, 29]-code), using
(83−28, 83, 18995)-Net over F32 — Digital
Digital (55, 83, 18995)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3283, 18995, F32, 28) (dual of [18995, 18912, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3283, 32775, F32, 28) (dual of [32775, 32692, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(3282, 32768, F32, 28) (dual of [32768, 32686, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3276, 32768, F32, 26) (dual of [32768, 32692, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3283, 32775, F32, 28) (dual of [32775, 32692, 29]-code), using
(83−28, 83, large)-Net in Base 32 — Upper bound on s
There is no (55, 83, large)-net in base 32, because
- 26 times m-reduction [i] would yield (55, 57, large)-net in base 32, but