Best Known (53−27, 53, s)-Nets in Base 128
(53−27, 53, 1260)-Net over F128 — Constructive and digital
Digital (26, 53, 1260)-net over F128, using
- net defined by OOA [i] based on linear OOA(12853, 1260, F128, 27, 27) (dual of [(1260, 27), 33967, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(12853, 16381, F128, 27) (dual of [16381, 16328, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(12853, 16384, F128, 27) (dual of [16384, 16331, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(12853, 16384, F128, 27) (dual of [16384, 16331, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(12853, 16381, F128, 27) (dual of [16381, 16328, 28]-code), using
(53−27, 53, 3509)-Net over F128 — Digital
Digital (26, 53, 3509)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12853, 3509, F128, 4, 27) (dual of [(3509, 4), 13983, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12853, 4096, F128, 4, 27) (dual of [(4096, 4), 16331, 28]-NRT-code), using
- OOA 4-folding [i] based on linear OA(12853, 16384, F128, 27) (dual of [16384, 16331, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- OOA 4-folding [i] based on linear OA(12853, 16384, F128, 27) (dual of [16384, 16331, 28]-code), using
- discarding factors / shortening the dual code based on linear OOA(12853, 4096, F128, 4, 27) (dual of [(4096, 4), 16331, 28]-NRT-code), using
(53−27, 53, large)-Net in Base 128 — Upper bound on s
There is no (26, 53, large)-net in base 128, because
- 25 times m-reduction [i] would yield (26, 28, large)-net in base 128, but