Best Known (86, 112, s)-Nets in Base 16
(86, 112, 10085)-Net over F16 — Constructive and digital
Digital (86, 112, 10085)-net over F16, using
- net defined by OOA [i] based on linear OOA(16112, 10085, F16, 26, 26) (dual of [(10085, 26), 262098, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(16112, 131105, F16, 26) (dual of [131105, 130993, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(16112, 131106, F16, 26) (dual of [131106, 130994, 27]-code), using
- trace code [i] based on linear OA(25656, 65553, F256, 26) (dual of [65553, 65497, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2565, 17, F256, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- Reed–Solomon code RS(251,256) [i]
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- trace code [i] based on linear OA(25656, 65553, F256, 26) (dual of [65553, 65497, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(16112, 131106, F16, 26) (dual of [131106, 130994, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(16112, 131105, F16, 26) (dual of [131105, 130993, 27]-code), using
(86, 112, 168277)-Net over F16 — Digital
Digital (86, 112, 168277)-net over F16, using
(86, 112, large)-Net in Base 16 — Upper bound on s
There is no (86, 112, large)-net in base 16, because
- 24 times m-reduction [i] would yield (86, 88, large)-net in base 16, but