Best Known (60, 60+18, s)-Nets in Base 27
(60, 60+18, 59077)-Net over F27 — Constructive and digital
Digital (60, 78, 59077)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 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 (51, 69, 59049)-net over F27, using
- net defined by OOA [i] based on linear OOA(2769, 59049, F27, 18, 18) (dual of [(59049, 18), 1062813, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2769, 531441, F27, 18) (dual of [531441, 531372, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- OA 9-folding and stacking [i] based on linear OA(2769, 531441, F27, 18) (dual of [531441, 531372, 19]-code), using
- net defined by OOA [i] based on linear OOA(2769, 59049, F27, 18, 18) (dual of [(59049, 18), 1062813, 19]-NRT-code), using
- digital (0, 9, 28)-net over F27, using
(60, 60+18, 1019552)-Net over F27 — Digital
Digital (60, 78, 1019552)-net over F27, using
(60, 60+18, large)-Net in Base 27 — Upper bound on s
There is no (60, 78, large)-net in base 27, because
- 16 times m-reduction [i] would yield (60, 62, large)-net in base 27, but