Best Known (61, 79, s)-Nets in Base 9
(61, 79, 1468)-Net over F9 — Constructive and digital
Digital (61, 79, 1468)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 10)-net over F9, using
- net from sequence [i] based on digital (0, 9)-sequence over F9, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 0 and N(F) ≥ 10, using
- the rational function field F9(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 9)-sequence over F9, using
- digital (52, 70, 1458)-net over F9, using
- net defined by OOA [i] based on linear OOA(970, 1458, F9, 18, 18) (dual of [(1458, 18), 26174, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(970, 13122, F9, 18) (dual of [13122, 13052, 19]-code), using
- trace code [i] based on linear OA(8135, 6561, F81, 18) (dual of [6561, 6526, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- trace code [i] based on linear OA(8135, 6561, F81, 18) (dual of [6561, 6526, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(970, 13122, F9, 18) (dual of [13122, 13052, 19]-code), using
- net defined by OOA [i] based on linear OOA(970, 1458, F9, 18, 18) (dual of [(1458, 18), 26174, 19]-NRT-code), using
- digital (0, 9, 10)-net over F9, using
(61, 79, 2187)-Net in Base 9 — Constructive
(61, 79, 2187)-net in base 9, using
- 91 times duplication [i] based on (60, 78, 2187)-net in base 9, using
- base change [i] based on digital (34, 52, 2187)-net over F27, using
- net defined by OOA [i] based on linear OOA(2752, 2187, F27, 18, 18) (dual of [(2187, 18), 39314, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2752, 19683, F27, 18) (dual of [19683, 19631, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- OA 9-folding and stacking [i] based on linear OA(2752, 19683, F27, 18) (dual of [19683, 19631, 19]-code), using
- net defined by OOA [i] based on linear OOA(2752, 2187, F27, 18, 18) (dual of [(2187, 18), 39314, 19]-NRT-code), using
- base change [i] based on digital (34, 52, 2187)-net over F27, using
(61, 79, 24402)-Net over F9 — Digital
Digital (61, 79, 24402)-net over F9, using
(61, 79, large)-Net in Base 9 — Upper bound on s
There is no (61, 79, large)-net in base 9, because
- 16 times m-reduction [i] would yield (61, 63, large)-net in base 9, but