Best Known (37, 75, s)-Nets in Base 128
(37, 75, 862)-Net over F128 — Constructive and digital
Digital (37, 75, 862)-net over F128, using
- net defined by OOA [i] based on linear OOA(12875, 862, F128, 38, 38) (dual of [(862, 38), 32681, 39]-NRT-code), using
- OA 19-folding and stacking [i] based on linear OA(12875, 16378, F128, 38) (dual of [16378, 16303, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(12875, 16384, F128, 38) (dual of [16384, 16309, 39]-code), using
- an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- discarding factors / shortening the dual code based on linear OA(12875, 16384, F128, 38) (dual of [16384, 16309, 39]-code), using
- OA 19-folding and stacking [i] based on linear OA(12875, 16378, F128, 38) (dual of [16378, 16303, 39]-code), using
(37, 75, 3526)-Net over F128 — Digital
Digital (37, 75, 3526)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12875, 3526, F128, 4, 38) (dual of [(3526, 4), 14029, 39]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12875, 4096, F128, 4, 38) (dual of [(4096, 4), 16309, 39]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12875, 16384, F128, 38) (dual of [16384, 16309, 39]-code), using
- an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- OOA 4-folding [i] based on linear OA(12875, 16384, F128, 38) (dual of [16384, 16309, 39]-code), using
- discarding factors / shortening the dual code based on linear OOA(12875, 4096, F128, 4, 38) (dual of [(4096, 4), 16309, 39]-NRT-code), using
(37, 75, large)-Net in Base 128 — Upper bound on s
There is no (37, 75, large)-net in base 128, because
- 36 times m-reduction [i] would yield (37, 39, large)-net in base 128, but