Best Known (49−8, 49, s)-Nets in Base 9
(49−8, 49, 265738)-Net over F9 — Constructive and digital
Digital (41, 49, 265738)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 16)-net over F9, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 1 and N(F) ≥ 16, using
- net from sequence [i] based on digital (1, 15)-sequence over F9, using
- digital (36, 44, 265722)-net over F9, using
- net defined by OOA [i] based on linear OOA(944, 265722, F9, 8, 8) (dual of [(265722, 8), 2125732, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(944, 1062888, F9, 8) (dual of [1062888, 1062844, 9]-code), using
- trace code [i] based on linear OA(8122, 531444, F81, 8) (dual of [531444, 531422, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(8122, 531441, F81, 8) (dual of [531441, 531419, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(8119, 531441, F81, 7) (dual of [531441, 531422, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- trace code [i] based on linear OA(8122, 531444, F81, 8) (dual of [531444, 531422, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(944, 1062888, F9, 8) (dual of [1062888, 1062844, 9]-code), using
- net defined by OOA [i] based on linear OOA(944, 265722, F9, 8, 8) (dual of [(265722, 8), 2125732, 9]-NRT-code), using
- digital (1, 5, 16)-net over F9, using
(49−8, 49, 2020817)-Net over F9 — Digital
Digital (41, 49, 2020817)-net over F9, using
(49−8, 49, large)-Net in Base 9 — Upper bound on s
There is no (41, 49, large)-net in base 9, because
- 6 times m-reduction [i] would yield (41, 43, large)-net in base 9, but