Best Known (92, 92+25, s)-Nets in Base 16
(92, 92+25, 87382)-Net over F16 — Constructive and digital
Digital (92, 117, 87382)-net over F16, using
- net defined by OOA [i] based on linear OOA(16117, 87382, F16, 25, 25) (dual of [(87382, 25), 2184433, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(16117, 1048585, F16, 25) (dual of [1048585, 1048468, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(16117, 1048587, F16, 25) (dual of [1048587, 1048470, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(16116, 1048576, F16, 25) (dual of [1048576, 1048460, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(16106, 1048576, F16, 23) (dual of [1048576, 1048470, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(161, 11, F16, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(16117, 1048587, F16, 25) (dual of [1048587, 1048470, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(16117, 1048585, F16, 25) (dual of [1048585, 1048468, 26]-code), using
(92, 92+25, 743551)-Net over F16 — Digital
Digital (92, 117, 743551)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16117, 743551, F16, 25) (dual of [743551, 743434, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(16117, 1048587, F16, 25) (dual of [1048587, 1048470, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(16116, 1048576, F16, 25) (dual of [1048576, 1048460, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(16106, 1048576, F16, 23) (dual of [1048576, 1048470, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(161, 11, F16, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(16117, 1048587, F16, 25) (dual of [1048587, 1048470, 26]-code), using
(92, 92+25, large)-Net in Base 16 — Upper bound on s
There is no (92, 117, large)-net in base 16, because
- 23 times m-reduction [i] would yield (92, 94, large)-net in base 16, but