Best Known (88−36, 88, s)-Nets in Base 27
(88−36, 88, 248)-Net over F27 — Constructive and digital
Digital (52, 88, 248)-net over F27, using
- 1 times m-reduction [i] based on digital (52, 89, 248)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (7, 19, 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, 25, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27 (see above)
- digital (8, 45, 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, 19, 82)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(88−36, 88, 398)-Net in Base 27 — Constructive
(52, 88, 398)-net in base 27, using
- (u, u+v)-construction [i] based on
- digital (0, 18, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- (34, 70, 370)-net in base 27, using
- 2 times m-reduction [i] based on (34, 72, 370)-net in base 27, using
- base change [i] based on digital (16, 54, 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, 54, 370)-net over F81, using
- 2 times m-reduction [i] based on (34, 72, 370)-net in base 27, using
- digital (0, 18, 28)-net over F27, using
(88−36, 88, 2141)-Net over F27 — Digital
Digital (52, 88, 2141)-net over F27, using
(88−36, 88, 2890238)-Net in Base 27 — Upper bound on s
There is no (52, 88, 2890239)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 912035 475331 112926 209014 089584 673798 223250 191783 927756 723536 353083 874880 223646 339540 889981 673587 526548 513565 225513 136427 201069 > 2788 [i]