Best Known (106−10, 106, s)-Nets in Base 7
(106−10, 106, 3357792)-Net over F7 — Constructive and digital
Digital (96, 106, 3357792)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (9, 14, 2352)-net over F7, using
- net defined by OOA [i] based on linear OOA(714, 2352, F7, 5, 5) (dual of [(2352, 5), 11746, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(714, 4705, F7, 5) (dual of [4705, 4691, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(714, 4706, F7, 5) (dual of [4706, 4692, 6]-code), using
- trace code [i] based on linear OA(497, 2353, F49, 5) (dual of [2353, 2346, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(714, 4706, F7, 5) (dual of [4706, 4692, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(714, 4705, F7, 5) (dual of [4705, 4691, 6]-code), using
- net defined by OOA [i] based on linear OOA(714, 2352, F7, 5, 5) (dual of [(2352, 5), 11746, 6]-NRT-code), using
- digital (82, 92, 3355440)-net over F7, using
- trace code for nets [i] based on digital (36, 46, 1677720)-net over F49, using
- net defined by OOA [i] based on linear OOA(4946, 1677720, F49, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(4946, 8388600, F49, 10) (dual of [8388600, 8388554, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(4946, large, F49, 10) (dual of [large, large−46, 11]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 25679568 | 495−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(4946, large, F49, 10) (dual of [large, large−46, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(4946, 8388600, F49, 10) (dual of [8388600, 8388554, 11]-code), using
- net defined by OOA [i] based on linear OOA(4946, 1677720, F49, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- trace code for nets [i] based on digital (36, 46, 1677720)-net over F49, using
- digital (9, 14, 2352)-net over F7, using
(106−10, 106, large)-Net over F7 — Digital
Digital (96, 106, large)-net over F7, using
- t-expansion [i] based on digital (94, 106, large)-net over F7, using
- 3 times m-reduction [i] based on digital (94, 109, large)-net over F7, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(7109, large, F7, 15) (dual of [large, large−109, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 20176804 | 718−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(7109, large, F7, 15) (dual of [large, large−109, 16]-code), using
- 3 times m-reduction [i] based on digital (94, 109, large)-net over F7, using
(106−10, 106, large)-Net in Base 7 — Upper bound on s
There is no (96, 106, large)-net in base 7, because
- 8 times m-reduction [i] would yield (96, 98, large)-net in base 7, but