Best Known (63, 63+22, s)-Nets in Base 32
(63, 63+22, 95325)-Net over F32 — Constructive and digital
Digital (63, 85, 95325)-net over F32, using
- net defined by OOA [i] based on linear OOA(3285, 95325, F32, 22, 22) (dual of [(95325, 22), 2097065, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3285, 1048575, F32, 22) (dual of [1048575, 1048490, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3285, 1048576, F32, 22) (dual of [1048576, 1048491, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(3285, 1048576, F32, 22) (dual of [1048576, 1048491, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3285, 1048575, F32, 22) (dual of [1048575, 1048490, 23]-code), using
(63, 63+22, 561781)-Net over F32 — Digital
Digital (63, 85, 561781)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3285, 561781, F32, 22) (dual of [561781, 561696, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3285, 1048576, F32, 22) (dual of [1048576, 1048491, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(3285, 1048576, F32, 22) (dual of [1048576, 1048491, 23]-code), using
(63, 63+22, large)-Net in Base 32 — Upper bound on s
There is no (63, 85, large)-net in base 32, because
- 20 times m-reduction [i] would yield (63, 65, large)-net in base 32, but