Best Known (64, 64+22, s)-Nets in Base 32
(64, 64+22, 95325)-Net over F32 — Constructive and digital
Digital (64, 86, 95325)-net over F32, using
- 321 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(3285, 95325, F32, 22, 22) (dual of [(95325, 22), 2097065, 23]-NRT-code), using
(64, 64+22, 668076)-Net over F32 — Digital
Digital (64, 86, 668076)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3286, 668076, F32, 22) (dual of [668076, 667990, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3286, 1048585, F32, 22) (dual of [1048585, 1048499, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] 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]
- linear OA(3277, 1048576, F32, 20) (dual of [1048576, 1048499, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(321, 9, F32, 1) (dual of [9, 8, 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(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3286, 1048585, F32, 22) (dual of [1048585, 1048499, 23]-code), using
(64, 64+22, large)-Net in Base 32 — Upper bound on s
There is no (64, 86, large)-net in base 32, because
- 20 times m-reduction [i] would yield (64, 66, large)-net in base 32, but