Best Known (65−29, 65, s)-Nets in Base 128
(65−29, 65, 1172)-Net over F128 — Constructive and digital
Digital (36, 65, 1172)-net over F128, using
- net defined by OOA [i] based on linear OOA(12865, 1172, F128, 29, 29) (dual of [(1172, 29), 33923, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(12865, 16409, F128, 29) (dual of [16409, 16344, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(12865, 16410, F128, 29) (dual of [16410, 16345, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(19) [i] based on
- linear OA(12857, 16384, F128, 29) (dual of [16384, 16327, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(12839, 16384, F128, 20) (dual of [16384, 16345, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1288, 26, F128, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,128)), using
- discarding factors / shortening the dual code based on linear OA(1288, 128, F128, 8) (dual of [128, 120, 9]-code or 128-arc in PG(7,128)), using
- Reed–Solomon code RS(120,128) [i]
- discarding factors / shortening the dual code based on linear OA(1288, 128, F128, 8) (dual of [128, 120, 9]-code or 128-arc in PG(7,128)), using
- construction X applied to Ce(28) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(12865, 16410, F128, 29) (dual of [16410, 16345, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(12865, 16409, F128, 29) (dual of [16409, 16344, 30]-code), using
(65−29, 65, 8488)-Net over F128 — Digital
Digital (36, 65, 8488)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12865, 8488, F128, 29) (dual of [8488, 8423, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(12865, 16410, F128, 29) (dual of [16410, 16345, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(19) [i] based on
- linear OA(12857, 16384, F128, 29) (dual of [16384, 16327, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(12839, 16384, F128, 20) (dual of [16384, 16345, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1288, 26, F128, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,128)), using
- discarding factors / shortening the dual code based on linear OA(1288, 128, F128, 8) (dual of [128, 120, 9]-code or 128-arc in PG(7,128)), using
- Reed–Solomon code RS(120,128) [i]
- discarding factors / shortening the dual code based on linear OA(1288, 128, F128, 8) (dual of [128, 120, 9]-code or 128-arc in PG(7,128)), using
- construction X applied to Ce(28) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(12865, 16410, F128, 29) (dual of [16410, 16345, 30]-code), using
(65−29, 65, large)-Net in Base 128 — Upper bound on s
There is no (36, 65, large)-net in base 128, because
- 27 times m-reduction [i] would yield (36, 38, large)-net in base 128, but