Best Known (81, 109, s)-Nets in Base 32
(81, 109, 74898)-Net over F32 — Constructive and digital
Digital (81, 109, 74898)-net over F32, using
- net defined by OOA [i] based on linear OOA(32109, 74898, F32, 28, 28) (dual of [(74898, 28), 2097035, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(32109, 1048572, F32, 28) (dual of [1048572, 1048463, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(32109, 1048576, F32, 28) (dual of [1048576, 1048467, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(32109, 1048576, F32, 28) (dual of [1048576, 1048467, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(32109, 1048572, F32, 28) (dual of [1048572, 1048463, 29]-code), using
(81, 109, 608252)-Net over F32 — Digital
Digital (81, 109, 608252)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(32109, 608252, F32, 28) (dual of [608252, 608143, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(32109, 1048576, F32, 28) (dual of [1048576, 1048467, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(32109, 1048576, F32, 28) (dual of [1048576, 1048467, 29]-code), using
(81, 109, large)-Net in Base 32 — Upper bound on s
There is no (81, 109, large)-net in base 32, because
- 26 times m-reduction [i] would yield (81, 83, large)-net in base 32, but