Best Known (34, 34+12, s)-Nets in Base 32
(34, 34+12, 174764)-Net over F32 — Constructive and digital
Digital (34, 46, 174764)-net over F32, using
- net defined by OOA [i] based on linear OOA(3246, 174764, F32, 12, 12) (dual of [(174764, 12), 2097122, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3246, 1048584, F32, 12) (dual of [1048584, 1048538, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3246, 1048585, F32, 12) (dual of [1048585, 1048539, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(3245, 1048576, F32, 12) (dual of [1048576, 1048531, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(3237, 1048576, F32, 10) (dual of [1048576, 1048539, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(3246, 1048585, F32, 12) (dual of [1048585, 1048539, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(3246, 1048584, F32, 12) (dual of [1048584, 1048538, 13]-code), using
(34, 34+12, 866537)-Net over F32 — Digital
Digital (34, 46, 866537)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3246, 866537, F32, 12) (dual of [866537, 866491, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3246, 1048585, F32, 12) (dual of [1048585, 1048539, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(3245, 1048576, F32, 12) (dual of [1048576, 1048531, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(3237, 1048576, F32, 10) (dual of [1048576, 1048539, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(3246, 1048585, F32, 12) (dual of [1048585, 1048539, 13]-code), using
(34, 34+12, large)-Net in Base 32 — Upper bound on s
There is no (34, 46, large)-net in base 32, because
- 10 times m-reduction [i] would yield (34, 36, large)-net in base 32, but