Best Known (62−35, 62, s)-Nets in Base 27
(62−35, 62, 140)-Net over F27 — Constructive and digital
Digital (27, 62, 140)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 21, 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 (6, 41, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (4, 21, 64)-net over F27, using
(62−35, 62, 172)-Net in Base 27 — Constructive
(27, 62, 172)-net in base 27, using
- 18 times m-reduction [i] based on (27, 80, 172)-net in base 27, using
- base change [i] based on digital (7, 60, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 60, 172)-net over F81, using
(62−35, 62, 211)-Net over F27 — Digital
Digital (27, 62, 211)-net over F27, using
(62−35, 62, 244)-Net in Base 27
(27, 62, 244)-net in base 27, using
- 10 times m-reduction [i] based on (27, 72, 244)-net in base 27, using
- base change [i] based on digital (9, 54, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- base change [i] based on digital (9, 54, 244)-net over F81, using
(62−35, 62, 37752)-Net in Base 27 — Upper bound on s
There is no (27, 62, 37753)-net in base 27, because
- 1 times m-reduction [i] would yield (27, 61, 37753)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 2057 526446 511932 617295 484051 570706 028858 720505 834900 013419 989668 659483 662111 957652 116619 > 2761 [i]