Best Known (13, 25, s)-Nets in Base 128
(13, 25, 2732)-Net over F128 — Constructive and digital
Digital (13, 25, 2732)-net over F128, using
- net defined by OOA [i] based on linear OOA(12825, 2732, F128, 12, 12) (dual of [(2732, 12), 32759, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(12825, 16392, F128, 12) (dual of [16392, 16367, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(12823, 16384, F128, 12) (dual of [16384, 16361, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(12817, 16384, F128, 9) (dual of [16384, 16367, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(1282, 8, F128, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- OA 6-folding and stacking [i] based on linear OA(12825, 16392, F128, 12) (dual of [16392, 16367, 13]-code), using
(13, 25, 7922)-Net over F128 — Digital
Digital (13, 25, 7922)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12825, 7922, F128, 2, 12) (dual of [(7922, 2), 15819, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12825, 8196, F128, 2, 12) (dual of [(8196, 2), 16367, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12825, 16392, F128, 12) (dual of [16392, 16367, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(12823, 16384, F128, 12) (dual of [16384, 16361, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(12817, 16384, F128, 9) (dual of [16384, 16367, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(1282, 8, F128, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- OOA 2-folding [i] based on linear OA(12825, 16392, F128, 12) (dual of [16392, 16367, 13]-code), using
- discarding factors / shortening the dual code based on linear OOA(12825, 8196, F128, 2, 12) (dual of [(8196, 2), 16367, 13]-NRT-code), using
(13, 25, large)-Net in Base 128 — Upper bound on s
There is no (13, 25, large)-net in base 128, because
- 10 times m-reduction [i] would yield (13, 15, large)-net in base 128, but