Best Known (32, 32+17, s)-Nets in Base 128
(32, 32+17, 262144)-Net over F128 — Constructive and digital
Digital (32, 49, 262144)-net over F128, using
- net defined by OOA [i] based on linear OOA(12849, 262144, F128, 17, 17) (dual of [(262144, 17), 4456399, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(12849, 2097153, F128, 17) (dual of [2097153, 2097104, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(12849, 2097153, F128, 17) (dual of [2097153, 2097104, 18]-code), using
(32, 32+17, 699051)-Net over F128 — Digital
Digital (32, 49, 699051)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12849, 699051, F128, 3, 17) (dual of [(699051, 3), 2097104, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12849, 2097153, F128, 17) (dual of [2097153, 2097104, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(12849, 2097153, F128, 17) (dual of [2097153, 2097104, 18]-code), using
(32, 32+17, large)-Net in Base 128 — Upper bound on s
There is no (32, 49, large)-net in base 128, because
- 15 times m-reduction [i] would yield (32, 34, large)-net in base 128, but