Best Known (53−24, 53, s)-Nets in Base 128
(53−24, 53, 1367)-Net over F128 — Constructive and digital
Digital (29, 53, 1367)-net over F128, using
- net defined by OOA [i] based on linear OOA(12853, 1367, F128, 24, 24) (dual of [(1367, 24), 32755, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(12853, 16404, F128, 24) (dual of [16404, 16351, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(16) [i] based on
- linear OA(12847, 16384, F128, 24) (dual of [16384, 16337, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(12833, 16384, F128, 17) (dual of [16384, 16351, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1286, 20, F128, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,128)), using
- discarding factors / shortening the dual code based on linear OA(1286, 128, F128, 6) (dual of [128, 122, 7]-code or 128-arc in PG(5,128)), using
- Reed–Solomon code RS(122,128) [i]
- discarding factors / shortening the dual code based on linear OA(1286, 128, F128, 6) (dual of [128, 122, 7]-code or 128-arc in PG(5,128)), using
- construction X applied to Ce(23) ⊂ Ce(16) [i] based on
- OA 12-folding and stacking [i] based on linear OA(12853, 16404, F128, 24) (dual of [16404, 16351, 25]-code), using
(53−24, 53, 8202)-Net over F128 — Digital
Digital (29, 53, 8202)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12853, 8202, F128, 2, 24) (dual of [(8202, 2), 16351, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12853, 16404, F128, 24) (dual of [16404, 16351, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(16) [i] based on
- linear OA(12847, 16384, F128, 24) (dual of [16384, 16337, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(12833, 16384, F128, 17) (dual of [16384, 16351, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1286, 20, F128, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,128)), using
- discarding factors / shortening the dual code based on linear OA(1286, 128, F128, 6) (dual of [128, 122, 7]-code or 128-arc in PG(5,128)), using
- Reed–Solomon code RS(122,128) [i]
- discarding factors / shortening the dual code based on linear OA(1286, 128, F128, 6) (dual of [128, 122, 7]-code or 128-arc in PG(5,128)), using
- construction X applied to Ce(23) ⊂ Ce(16) [i] based on
- OOA 2-folding [i] based on linear OA(12853, 16404, F128, 24) (dual of [16404, 16351, 25]-code), using
(53−24, 53, large)-Net in Base 128 — Upper bound on s
There is no (29, 53, large)-net in base 128, because
- 22 times m-reduction [i] would yield (29, 31, large)-net in base 128, but