Best Known (63−18, 63, s)-Nets in Base 27
(63−18, 63, 2235)-Net over F27 — Constructive and digital
Digital (45, 63, 2235)-net over F27, using
- (u, u+v)-construction [i] based on
- 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 (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 (2, 11, 48)-net over F27, using
(63−18, 63, 55655)-Net over F27 — Digital
Digital (45, 63, 55655)-net over F27, using
(63−18, 63, large)-Net in Base 27 — Upper bound on s
There is no (45, 63, large)-net in base 27, because
- 16 times m-reduction [i] would yield (45, 47, large)-net in base 27, but