Best Known (114−28, 114, s)-Nets in Base 16
(114−28, 114, 9363)-Net over F16 — Constructive and digital
Digital (86, 114, 9363)-net over F16, using
- 162 times duplication [i] based on digital (84, 112, 9363)-net over F16, using
- net defined by OOA [i] based on linear OOA(16112, 9363, F16, 28, 28) (dual of [(9363, 28), 262052, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(16112, 131082, F16, 28) (dual of [131082, 130970, 29]-code), using
- trace code [i] based on linear OA(25656, 65541, F256, 28) (dual of [65541, 65485, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- 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(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- trace code [i] based on linear OA(25656, 65541, F256, 28) (dual of [65541, 65485, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(16112, 131082, F16, 28) (dual of [131082, 130970, 29]-code), using
- net defined by OOA [i] based on linear OOA(16112, 9363, F16, 28, 28) (dual of [(9363, 28), 262052, 29]-NRT-code), using
(114−28, 114, 120349)-Net over F16 — Digital
Digital (86, 114, 120349)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16114, 120349, F16, 28) (dual of [120349, 120235, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(16114, 131088, F16, 28) (dual of [131088, 130974, 29]-code), using
- trace code [i] based on linear OA(25657, 65544, F256, 28) (dual of [65544, 65487, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(25649, 65536, F256, 25) (dual of [65536, 65487, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- trace code [i] based on linear OA(25657, 65544, F256, 28) (dual of [65544, 65487, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(16114, 131088, F16, 28) (dual of [131088, 130974, 29]-code), using
(114−28, 114, large)-Net in Base 16 — Upper bound on s
There is no (86, 114, large)-net in base 16, because
- 26 times m-reduction [i] would yield (86, 88, large)-net in base 16, but