Best Known (37−26, 37, s)-Nets in Base 27
(37−26, 37, 96)-Net over F27 — Constructive and digital
Digital (11, 37, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
(37−26, 37, 100)-Net in Base 27 — Constructive
(11, 37, 100)-net in base 27, using
- 3 times m-reduction [i] based on (11, 40, 100)-net in base 27, using
- base change [i] based on digital (1, 30, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- base change [i] based on digital (1, 30, 100)-net over F81, using
(37−26, 37, 100)-Net over F27 — Digital
Digital (11, 37, 100)-net over F27, using
- net from sequence [i] based on digital (11, 99)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 100, using
(37−26, 37, 2577)-Net in Base 27 — Upper bound on s
There is no (11, 37, 2578)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 91465 989272 007172 166938 591296 815947 692301 882162 555677 > 2737 [i]