Best Known (38, 38+47, s)-Nets in Base 27
(38, 38+47, 166)-Net over F27 — Constructive and digital
Digital (38, 85, 166)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 30, 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, 55, 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, 30, 82)-net over F27, using
(38, 38+47, 301)-Net over F27 — Digital
Digital (38, 85, 301)-net over F27, using
(38, 38+47, 370)-Net in Base 27 — Constructive
(38, 85, 370)-net in base 27, using
- 3 times m-reduction [i] based on (38, 88, 370)-net in base 27, using
- base change [i] based on digital (16, 66, 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, 66, 370)-net over F81, using
(38, 38+47, 61233)-Net in Base 27 — Upper bound on s
There is no (38, 85, 61234)-net in base 27, because
- 1 times m-reduction [i] would yield (38, 84, 61234)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1 716569 775779 548368 980020 529121 077982 121798 159668 883785 230111 684413 840453 677603 648139 866967 635242 803776 594562 849367 655609 > 2784 [i]