Best Known (40, 40+64, s)-Nets in Base 27
(40, 40+64, 128)-Net over F27 — Constructive and digital
Digital (40, 104, 128)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 36, 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 (4, 68, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 36, 64)-net over F27, using
(40, 40+64, 224)-Net in Base 27 — Constructive
(40, 104, 224)-net in base 27, using
- 4 times m-reduction [i] based on (40, 108, 224)-net in base 27, using
- base change [i] based on digital (13, 81, 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, 81, 224)-net over F81, using
(40, 40+64, 273)-Net over F27 — Digital
Digital (40, 104, 273)-net over F27, using
- net from sequence [i] based on digital (40, 272)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 40 and N(F) ≥ 273, using
(40, 40+64, 298)-Net in Base 27
(40, 104, 298)-net in base 27, using
- t-expansion [i] based on (39, 104, 298)-net in base 27, using
- 4 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
- 4 times m-reduction [i] based on (39, 108, 298)-net in base 27, using
(40, 40+64, 22055)-Net in Base 27 — Upper bound on s
There is no (40, 104, 22056)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 72839 628246 060988 630100 136559 341657 505066 444062 687589 332557 734215 164018 580436 937579 158669 718980 698281 152109 346862 216900 793527 557219 052039 109741 207553 > 27104 [i]