Best Known (94−32, 94, s)-Nets in Base 32
(94−32, 94, 2048)-Net over F32 — Constructive and digital
Digital (62, 94, 2048)-net over F32, using
- net defined by OOA [i] based on linear OOA(3294, 2048, F32, 32, 32) (dual of [(2048, 32), 65442, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(3294, 32768, F32, 32) (dual of [32768, 32674, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3294, 32771, F32, 32) (dual of [32771, 32677, 33]-code), using
- 1 times truncation [i] based on linear OA(3295, 32772, F32, 33) (dual of [32772, 32677, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(30) [i] based on
- linear OA(3294, 32768, F32, 33) (dual of [32768, 32674, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3291, 32768, F32, 31) (dual of [32768, 32677, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(321, 4, F32, 1) (dual of [4, 3, 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(32) ⊂ Ce(30) [i] based on
- 1 times truncation [i] based on linear OA(3295, 32772, F32, 33) (dual of [32772, 32677, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(3294, 32771, F32, 32) (dual of [32771, 32677, 33]-code), using
- OA 16-folding and stacking [i] based on linear OA(3294, 32768, F32, 32) (dual of [32768, 32674, 33]-code), using
(94−32, 94, 17990)-Net over F32 — Digital
Digital (62, 94, 17990)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3294, 17990, F32, 32) (dual of [17990, 17896, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3294, 32771, F32, 32) (dual of [32771, 32677, 33]-code), using
- 1 times truncation [i] based on linear OA(3295, 32772, F32, 33) (dual of [32772, 32677, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(30) [i] based on
- linear OA(3294, 32768, F32, 33) (dual of [32768, 32674, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(3291, 32768, F32, 31) (dual of [32768, 32677, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(321, 4, F32, 1) (dual of [4, 3, 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(32) ⊂ Ce(30) [i] based on
- 1 times truncation [i] based on linear OA(3295, 32772, F32, 33) (dual of [32772, 32677, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(3294, 32771, F32, 32) (dual of [32771, 32677, 33]-code), using
(94−32, 94, large)-Net in Base 32 — Upper bound on s
There is no (62, 94, large)-net in base 32, because
- 30 times m-reduction [i] would yield (62, 64, large)-net in base 32, but