Best Known (40, 91, s)-Nets in Base 27
(40, 91, 166)-Net over F27 — Constructive and digital
Digital (40, 91, 166)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 32, 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 (8, 59, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- digital (7, 32, 82)-net over F27, using
(40, 91, 294)-Net over F27 — Digital
Digital (40, 91, 294)-net over F27, using
(40, 91, 370)-Net in Base 27 — Constructive
(40, 91, 370)-net in base 27, using
- 5 times m-reduction [i] based on (40, 96, 370)-net in base 27, using
- base change [i] based on digital (16, 72, 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, 72, 370)-net over F81, using
(40, 91, 55649)-Net in Base 27 — Upper bound on s
There is no (40, 91, 55650)-net in base 27, because
- 1 times m-reduction [i] would yield (40, 90, 55650)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 665 036706 587689 798380 924633 247178 362546 397335 529195 550543 830878 643418 593020 231973 403882 640519 377941 777547 562748 808951 042518 169477 > 2790 [i]