Best Known (22−8, 22, s)-Nets in Base 32
(22−8, 22, 8192)-Net over F32 — Constructive and digital
Digital (14, 22, 8192)-net over F32, using
- net defined by OOA [i] based on linear OOA(3222, 8192, F32, 8, 8) (dual of [(8192, 8), 65514, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(3222, 32768, F32, 8) (dual of [32768, 32746, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OA 4-folding and stacking [i] based on linear OA(3222, 32768, F32, 8) (dual of [32768, 32746, 9]-code), using
(22−8, 22, 17899)-Net over F32 — Digital
Digital (14, 22, 17899)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3222, 17899, F32, 8) (dual of [17899, 17877, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(3222, 32768, F32, 8) (dual of [32768, 32746, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(3222, 32768, F32, 8) (dual of [32768, 32746, 9]-code), using
(22−8, 22, large)-Net in Base 32 — Upper bound on s
There is no (14, 22, large)-net in base 32, because
- 6 times m-reduction [i] would yield (14, 16, large)-net in base 32, but