Best Known (38, 77, s)-Nets in Base 128
(38, 77, 862)-Net over F128 — Constructive and digital
Digital (38, 77, 862)-net over F128, using
- net defined by OOA [i] based on linear OOA(12877, 862, F128, 39, 39) (dual of [(862, 39), 33541, 40]-NRT-code), using
- OOA 19-folding and stacking with additional row [i] based on linear OA(12877, 16379, F128, 39) (dual of [16379, 16302, 40]-code), using
- discarding factors / shortening the dual code based on linear OA(12877, 16384, F128, 39) (dual of [16384, 16307, 40]-code), using
- an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- discarding factors / shortening the dual code based on linear OA(12877, 16384, F128, 39) (dual of [16384, 16307, 40]-code), using
- OOA 19-folding and stacking with additional row [i] based on linear OA(12877, 16379, F128, 39) (dual of [16379, 16302, 40]-code), using
(38, 77, 3548)-Net over F128 — Digital
Digital (38, 77, 3548)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12877, 3548, F128, 4, 39) (dual of [(3548, 4), 14115, 40]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12877, 4096, F128, 4, 39) (dual of [(4096, 4), 16307, 40]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12877, 16384, F128, 39) (dual of [16384, 16307, 40]-code), using
- an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- OOA 4-folding [i] based on linear OA(12877, 16384, F128, 39) (dual of [16384, 16307, 40]-code), using
- discarding factors / shortening the dual code based on linear OOA(12877, 4096, F128, 4, 39) (dual of [(4096, 4), 16307, 40]-NRT-code), using
(38, 77, large)-Net in Base 128 — Upper bound on s
There is no (38, 77, large)-net in base 128, because
- 37 times m-reduction [i] would yield (38, 40, large)-net in base 128, but