Best Known (96, 122, s)-Nets in Base 16
(96, 122, 80660)-Net over F16 — Constructive and digital
Digital (96, 122, 80660)-net over F16, using
- 161 times duplication [i] based on digital (95, 121, 80660)-net over F16, using
- net defined by OOA [i] based on linear OOA(16121, 80660, F16, 26, 26) (dual of [(80660, 26), 2097039, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(16121, 1048580, F16, 26) (dual of [1048580, 1048459, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(16121, 1048581, F16, 26) (dual of [1048581, 1048460, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(16121, 1048576, F16, 26) (dual of [1048576, 1048455, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- 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(160, 5, F16, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(16121, 1048581, F16, 26) (dual of [1048581, 1048460, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(16121, 1048580, F16, 26) (dual of [1048580, 1048459, 27]-code), using
- net defined by OOA [i] based on linear OOA(16121, 80660, F16, 26, 26) (dual of [(80660, 26), 2097039, 27]-NRT-code), using
(96, 122, 769194)-Net over F16 — Digital
Digital (96, 122, 769194)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16122, 769194, F16, 26) (dual of [769194, 769072, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(16122, 1048587, F16, 26) (dual of [1048587, 1048465, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(23) [i] based on
- linear OA(16121, 1048576, F16, 26) (dual of [1048576, 1048455, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(16111, 1048576, F16, 24) (dual of [1048576, 1048465, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(25) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(16122, 1048587, F16, 26) (dual of [1048587, 1048465, 27]-code), using
(96, 122, large)-Net in Base 16 — Upper bound on s
There is no (96, 122, large)-net in base 16, because
- 24 times m-reduction [i] would yield (96, 98, large)-net in base 16, but