Best Known (116−25, 116, s)-Nets in Base 16
(116−25, 116, 87381)-Net over F16 — Constructive and digital
Digital (91, 116, 87381)-net over F16, using
- net defined by OOA [i] based on linear OOA(16116, 87381, F16, 25, 25) (dual of [(87381, 25), 2184409, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(16116, 1048573, F16, 25) (dual of [1048573, 1048457, 26]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(16116, 1048576, F16, 25) (dual of [1048576, 1048460, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(16116, 1048573, F16, 25) (dual of [1048573, 1048457, 26]-code), using
(116−25, 116, 659109)-Net over F16 — Digital
Digital (91, 116, 659109)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16116, 659109, F16, 25) (dual of [659109, 658993, 26]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(16116, 1048576, F16, 25) (dual of [1048576, 1048460, 26]-code), using
(116−25, 116, large)-Net in Base 16 — Upper bound on s
There is no (91, 116, large)-net in base 16, because
- 23 times m-reduction [i] would yield (91, 93, large)-net in base 16, but