Best Known (50, 50+18, s)-Nets in Base 27
(50, 50+18, 2273)-Net over F27 — Constructive and digital
Digital (50, 68, 2273)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 16, 86)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- digital (2, 11, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- digital (1, 5, 38)-net over F27, using
- (u, u+v)-construction [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
- digital (7, 16, 86)-net over F27, using
(50, 50+18, 2303)-Net in Base 27 — Constructive
(50, 68, 2303)-net in base 27, using
- 271 times duplication [i] based on (49, 67, 2303)-net in base 27, using
- (u, u+v)-construction [i] based on
- (6, 15, 116)-net in base 27, using
- 1 times m-reduction [i] based on (6, 16, 116)-net in base 27, using
- base change [i] based on digital (2, 12, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 12, 116)-net over F81, using
- 1 times m-reduction [i] based on (6, 16, 116)-net in base 27, using
- 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
- (6, 15, 116)-net in base 27, using
- (u, u+v)-construction [i] based on
(50, 50+18, 146707)-Net over F27 — Digital
Digital (50, 68, 146707)-net over F27, using
(50, 50+18, large)-Net in Base 27 — Upper bound on s
There is no (50, 68, large)-net in base 27, because
- 16 times m-reduction [i] would yield (50, 52, large)-net in base 27, but