Best Known (73, 73+26, s)-Nets in Base 27
(73, 73+26, 1610)-Net over F27 — Constructive and digital
Digital (73, 99, 1610)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (10, 23, 96)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (2, 8, 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 (2, 15, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27 (see above)
- digital (2, 8, 48)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (50, 76, 1514)-net over F27, using
- net defined by OOA [i] based on linear OOA(2776, 1514, F27, 26, 26) (dual of [(1514, 26), 39288, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(2776, 19682, F27, 26) (dual of [19682, 19606, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2776, 19683, F27, 26) (dual of [19683, 19607, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(2776, 19683, F27, 26) (dual of [19683, 19607, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(2776, 19682, F27, 26) (dual of [19682, 19606, 27]-code), using
- net defined by OOA [i] based on linear OOA(2776, 1514, F27, 26, 26) (dual of [(1514, 26), 39288, 27]-NRT-code), using
- digital (10, 23, 96)-net over F27, using
(73, 73+26, 1664)-Net in Base 27 — Constructive
(73, 99, 1664)-net in base 27, using
- (u, u+v)-construction [i] based on
- (10, 23, 150)-net in base 27, using
- 1 times m-reduction [i] based on (10, 24, 150)-net in base 27, using
- base change [i] based on digital (4, 18, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- base change [i] based on digital (4, 18, 150)-net over F81, using
- 1 times m-reduction [i] based on (10, 24, 150)-net in base 27, using
- digital (50, 76, 1514)-net over F27, using
- net defined by OOA [i] based on linear OOA(2776, 1514, F27, 26, 26) (dual of [(1514, 26), 39288, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(2776, 19682, F27, 26) (dual of [19682, 19606, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2776, 19683, F27, 26) (dual of [19683, 19607, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(2776, 19683, F27, 26) (dual of [19683, 19607, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(2776, 19682, F27, 26) (dual of [19682, 19606, 27]-code), using
- net defined by OOA [i] based on linear OOA(2776, 1514, F27, 26, 26) (dual of [(1514, 26), 39288, 27]-NRT-code), using
- (10, 23, 150)-net in base 27, using
(73, 73+26, 182340)-Net over F27 — Digital
Digital (73, 99, 182340)-net over F27, using
(73, 73+26, large)-Net in Base 27 — Upper bound on s
There is no (73, 99, large)-net in base 27, because
- 24 times m-reduction [i] would yield (73, 75, large)-net in base 27, but