Best Known (29, 37, s)-Nets in Base 32
(29, 37, 2097150)-Net over F32 — Constructive and digital
Digital (29, 37, 2097150)-net over F32, using
- 321 times duplication [i] based on digital (28, 36, 2097150)-net over F32, using
- net defined by OOA [i] based on linear OOA(3236, 2097150, F32, 8, 8) (dual of [(2097150, 8), 16777164, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(3236, 8388600, F32, 8) (dual of [8388600, 8388564, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, large, F32, 8) (dual of [large, large−36, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(3236, large, F32, 8) (dual of [large, large−36, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(3236, 8388600, F32, 8) (dual of [8388600, 8388564, 9]-code), using
- net defined by OOA [i] based on linear OOA(3236, 2097150, F32, 8, 8) (dual of [(2097150, 8), 16777164, 9]-NRT-code), using
(29, 37, large)-Net over F32 — Digital
Digital (29, 37, large)-net over F32, using
- 321 times duplication [i] based on digital (28, 36, large)-net over F32, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3236, large, F32, 8) (dual of [large, large−36, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3236, large, F32, 8) (dual of [large, large−36, 9]-code), using
(29, 37, large)-Net in Base 32 — Upper bound on s
There is no (29, 37, large)-net in base 32, because
- 6 times m-reduction [i] would yield (29, 31, large)-net in base 32, but