Best Known (130−33, 130, s)-Nets in Base 16
(130−33, 130, 8192)-Net over F16 — Constructive and digital
Digital (97, 130, 8192)-net over F16, using
- net defined by OOA [i] based on linear OOA(16130, 8192, F16, 33, 33) (dual of [(8192, 33), 270206, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(16130, 131073, F16, 33) (dual of [131073, 130943, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(16130, 131074, F16, 33) (dual of [131074, 130944, 34]-code), using
- trace code [i] based on linear OA(25665, 65537, F256, 33) (dual of [65537, 65472, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- trace code [i] based on linear OA(25665, 65537, F256, 33) (dual of [65537, 65472, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(16130, 131074, F16, 33) (dual of [131074, 130944, 34]-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(16130, 131073, F16, 33) (dual of [131073, 130943, 34]-code), using
(130−33, 130, 84830)-Net over F16 — Digital
Digital (97, 130, 84830)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16130, 84830, F16, 33) (dual of [84830, 84700, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(16130, 131074, F16, 33) (dual of [131074, 130944, 34]-code), using
- trace code [i] based on linear OA(25665, 65537, F256, 33) (dual of [65537, 65472, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- trace code [i] based on linear OA(25665, 65537, F256, 33) (dual of [65537, 65472, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(16130, 131074, F16, 33) (dual of [131074, 130944, 34]-code), using
(130−33, 130, large)-Net in Base 16 — Upper bound on s
There is no (97, 130, large)-net in base 16, because
- 31 times m-reduction [i] would yield (97, 99, large)-net in base 16, but