Best Known (101−10, 101, s)-Nets in Base 7
(101−10, 101, 3355490)-Net over F7 — Constructive and digital
Digital (91, 101, 3355490)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (4, 9, 50)-net over F7, using
- base reduction for projective spaces (embedding PG(4,49) in PG(8,7)) for nets [i] based on digital (0, 5, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- base reduction for projective spaces (embedding PG(4,49) in PG(8,7)) for nets [i] based on digital (0, 5, 50)-net over F49, 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 (4, 9, 50)-net over F7, using
(101−10, 101, large)-Net over F7 — Digital
Digital (91, 101, large)-net over F7, using
- 73 times duplication [i] based on digital (88, 98, large)-net over F7, using
- t-expansion [i] based on digital (85, 98, large)-net over F7, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(798, large, F7, 13) (dual of [large, large−98, 14]-code), using
- trace code [i] based on linear OA(4949, 5764802, F49, 13) (dual of [5764802, 5764753, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- trace code [i] based on linear OA(4949, 5764802, F49, 13) (dual of [5764802, 5764753, 14]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(798, large, F7, 13) (dual of [large, large−98, 14]-code), using
- t-expansion [i] based on digital (85, 98, large)-net over F7, using
(101−10, 101, large)-Net in Base 7 — Upper bound on s
There is no (91, 101, large)-net in base 7, because
- 8 times m-reduction [i] would yield (91, 93, large)-net in base 7, but