Best Known (85, 85+28, s)-Nets in Base 16
(85, 85+28, 9363)-Net over F16 — Constructive and digital
Digital (85, 113, 9363)-net over F16, using
- 161 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
(85, 85+28, 108175)-Net over F16 — Digital
Digital (85, 113, 108175)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16113, 108175, F16, 28) (dual of [108175, 108062, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(16113, 131083, F16, 28) (dual of [131083, 130970, 29]-code), using
- 1 times code embedding in larger space [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
- 1 times code embedding in larger space [i] based on linear OA(16112, 131082, F16, 28) (dual of [131082, 130970, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(16113, 131083, F16, 28) (dual of [131083, 130970, 29]-code), using
(85, 85+28, large)-Net in Base 16 — Upper bound on s
There is no (85, 113, large)-net in base 16, because
- 26 times m-reduction [i] would yield (85, 87, large)-net in base 16, but