Best Known (79, 106, s)-Nets in Base 16
(79, 106, 10082)-Net over F16 — Constructive and digital
Digital (79, 106, 10082)-net over F16, using
- net defined by OOA [i] based on linear OOA(16106, 10082, F16, 27, 27) (dual of [(10082, 27), 272108, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(16106, 131067, F16, 27) (dual of [131067, 130961, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(16106, 131074, F16, 27) (dual of [131074, 130968, 28]-code), using
- trace code [i] based on linear OA(25653, 65537, F256, 27) (dual of [65537, 65484, 28]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- trace code [i] based on linear OA(25653, 65537, F256, 27) (dual of [65537, 65484, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(16106, 131074, F16, 27) (dual of [131074, 130968, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(16106, 131067, F16, 27) (dual of [131067, 130961, 28]-code), using
(79, 106, 77404)-Net over F16 — Digital
Digital (79, 106, 77404)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16106, 77404, F16, 27) (dual of [77404, 77298, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(16106, 131074, F16, 27) (dual of [131074, 130968, 28]-code), using
- trace code [i] based on linear OA(25653, 65537, F256, 27) (dual of [65537, 65484, 28]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- trace code [i] based on linear OA(25653, 65537, F256, 27) (dual of [65537, 65484, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(16106, 131074, F16, 27) (dual of [131074, 130968, 28]-code), using
(79, 106, large)-Net in Base 16 — Upper bound on s
There is no (79, 106, large)-net in base 16, because
- 25 times m-reduction [i] would yield (79, 81, large)-net in base 16, but