Best Known (39, 39+56, s)-Nets in Base 27
(39, 39+56, 146)-Net over F27 — Constructive and digital
Digital (39, 95, 146)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 32, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (7, 63, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (4, 32, 64)-net over F27, using
(39, 39+56, 224)-Net in Base 27 — Constructive
(39, 95, 224)-net in base 27, using
- 9 times m-reduction [i] based on (39, 104, 224)-net in base 27, using
- base change [i] based on digital (13, 78, 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, 78, 224)-net over F81, using
(39, 39+56, 271)-Net over F27 — Digital
Digital (39, 95, 271)-net over F27, using
- net from sequence [i] based on digital (39, 270)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 39 and N(F) ≥ 271, using
(39, 39+56, 298)-Net in Base 27
(39, 95, 298)-net in base 27, using
- 13 times m-reduction [i] based on (39, 108, 298)-net in base 27, using
- base change [i] based on digital (12, 81, 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, 81, 298)-net over F81, using
(39, 39+56, 31206)-Net in Base 27 — Upper bound on s
There is no (39, 95, 31207)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 9546 577197 129298 548205 390194 434027 399289 092454 139908 857038 093104 934757 029320 606346 170567 162921 126889 242384 597032 413279 733456 140420 144425 > 2795 [i]