Best Known (34, 34+14, s)-Nets in Base 7
(34, 34+14, 343)-Net over F7 — Constructive and digital
Digital (34, 48, 343)-net over F7, using
- net defined by OOA [i] based on linear OOA(748, 343, F7, 14, 14) (dual of [(343, 14), 4754, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(748, 2401, F7, 14) (dual of [2401, 2353, 15]-code), using
- 1 times truncation [i] based on linear OA(749, 2402, F7, 15) (dual of [2402, 2353, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2402 | 78−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(749, 2402, F7, 15) (dual of [2402, 2353, 16]-code), using
- OA 7-folding and stacking [i] based on linear OA(748, 2401, F7, 14) (dual of [2401, 2353, 15]-code), using
(34, 34+14, 1793)-Net over F7 — Digital
Digital (34, 48, 1793)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(748, 1793, F7, 14) (dual of [1793, 1745, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(748, 2401, F7, 14) (dual of [2401, 2353, 15]-code), using
- 1 times truncation [i] based on linear OA(749, 2402, F7, 15) (dual of [2402, 2353, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2402 | 78−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(749, 2402, F7, 15) (dual of [2402, 2353, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(748, 2401, F7, 14) (dual of [2401, 2353, 15]-code), using
(34, 34+14, 351334)-Net in Base 7 — Upper bound on s
There is no (34, 48, 351335)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 36704 066592 959811 893020 203707 037155 740183 > 748 [i]