Best Known (38, 91, s)-Nets in Base 27
(38, 91, 152)-Net over F27 — Constructive and digital
Digital (38, 91, 152)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 32, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (6, 59, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 32, 76)-net over F27, using
(38, 91, 224)-Net in Base 27 — Constructive
(38, 91, 224)-net in base 27, using
- 9 times m-reduction [i] based on (38, 100, 224)-net in base 27, using
- base change [i] based on digital (13, 75, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- base change [i] based on digital (13, 75, 224)-net over F81, using
(38, 91, 244)-Net over F27 — Digital
Digital (38, 91, 244)-net over F27, using
- t-expansion [i] based on digital (36, 91, 244)-net over F27, using
- net from sequence [i] based on digital (36, 243)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 36 and N(F) ≥ 244, using
- net from sequence [i] based on digital (36, 243)-sequence over F27, using
(38, 91, 298)-Net in Base 27
(38, 91, 298)-net in base 27, using
- 13 times m-reduction [i] based on (38, 104, 298)-net in base 27, using
- base change [i] based on digital (12, 78, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- base change [i] based on digital (12, 78, 298)-net over F81, using
(38, 91, 36549)-Net in Base 27 — Upper bound on s
There is no (38, 91, 36550)-net in base 27, because
- 1 times m-reduction [i] would yield (38, 90, 36550)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 665 165123 369666 978786 372186 424893 365932 656947 521857 788433 804208 239504 324059 484006 127702 946825 085027 418580 941452 357233 223146 869213 > 2790 [i]