Best Known (53, 53+15, s)-Nets in Base 27
(53, 53+15, 75986)-Net over F27 — Constructive and digital
Digital (53, 68, 75986)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 11, 66)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- digital (1, 8, 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 (0, 3, 28)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (42, 57, 75920)-net over F27, using
- net defined by OOA [i] based on linear OOA(2757, 75920, F27, 15, 15) (dual of [(75920, 15), 1138743, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2757, 531441, F27, 15) (dual of [531441, 531384, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- OOA 7-folding and stacking with additional row [i] based on linear OA(2757, 531441, F27, 15) (dual of [531441, 531384, 16]-code), using
- net defined by OOA [i] based on linear OOA(2757, 75920, F27, 15, 15) (dual of [(75920, 15), 1138743, 16]-NRT-code), using
- digital (4, 11, 66)-net over F27, using
(53, 53+15, 76020)-Net in Base 27 — Constructive
(53, 68, 76020)-net in base 27, using
- base change [i] based on digital (36, 51, 76020)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- digital (28, 43, 75920)-net over F81, using
- net defined by OOA [i] based on linear OOA(8143, 75920, F81, 15, 15) (dual of [(75920, 15), 1138757, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(8143, 531441, F81, 15) (dual of [531441, 531398, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- OOA 7-folding and stacking with additional row [i] based on linear OA(8143, 531441, F81, 15) (dual of [531441, 531398, 16]-code), using
- net defined by OOA [i] based on linear OOA(8143, 75920, F81, 15, 15) (dual of [(75920, 15), 1138757, 16]-NRT-code), using
- digital (1, 8, 100)-net over F81, using
- (u, u+v)-construction [i] based on
(53, 53+15, 2083647)-Net over F27 — Digital
Digital (53, 68, 2083647)-net over F27, using
(53, 53+15, large)-Net in Base 27 — Upper bound on s
There is no (53, 68, large)-net in base 27, because
- 13 times m-reduction [i] would yield (53, 55, large)-net in base 27, but