Best Known (38, 76, s)-Nets in Base 128
(38, 76, 862)-Net over F128 — Constructive and digital
Digital (38, 76, 862)-net over F128, using
- 1 times m-reduction [i] based on 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
- net defined by OOA [i] based on linear OOA(12877, 862, F128, 39, 39) (dual of [(862, 39), 33541, 40]-NRT-code), using
(38, 76, 4087)-Net over F128 — Digital
Digital (38, 76, 4087)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12876, 4087, F128, 4, 38) (dual of [(4087, 4), 16272, 39]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12876, 4097, F128, 4, 38) (dual of [(4097, 4), 16312, 39]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12876, 16388, F128, 38) (dual of [16388, 16312, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(12876, 16389, F128, 38) (dual of [16389, 16313, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(35) [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]
- linear OA(12871, 16384, F128, 36) (dual of [16384, 16313, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(37) ⊂ Ce(35) [i] based on
- discarding factors / shortening the dual code based on linear OA(12876, 16389, F128, 38) (dual of [16389, 16313, 39]-code), using
- OOA 4-folding [i] based on linear OA(12876, 16388, F128, 38) (dual of [16388, 16312, 39]-code), using
- discarding factors / shortening the dual code based on linear OOA(12876, 4097, F128, 4, 38) (dual of [(4097, 4), 16312, 39]-NRT-code), using
(38, 76, large)-Net in Base 128 — Upper bound on s
There is no (38, 76, large)-net in base 128, because
- 36 times m-reduction [i] would yield (38, 40, large)-net in base 128, but