Best Known (42, 42+57, s)-Nets in Base 27
(42, 42+57, 164)-Net over F27 — Constructive and digital
Digital (42, 99, 164)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 35, 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 (7, 64, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27 (see above)
- digital (7, 35, 82)-net over F27, using
(42, 42+57, 280)-Net over F27 — Digital
Digital (42, 99, 280)-net over F27, using
- net from sequence [i] based on digital (42, 279)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 42 and N(F) ≥ 280, using
(42, 42+57, 370)-Net in Base 27 — Constructive
(42, 99, 370)-net in base 27, using
- 5 times m-reduction [i] based on (42, 104, 370)-net in base 27, using
- base change [i] based on digital (16, 78, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 78, 370)-net over F81, using
(42, 42+57, 44428)-Net in Base 27 — Upper bound on s
There is no (42, 99, 44429)-net in base 27, because
- 1 times m-reduction [i] would yield (42, 98, 44429)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 187 829913 725959 075022 907084 554036 504814 751323 660330 107863 716023 358828 977613 738342 919247 489243 425592 647209 453662 838431 993624 627378 298067 376017 > 2798 [i]