Best Known (108−66, 108, s)-Nets in Base 27
(108−66, 108, 132)-Net over F27 — Constructive and digital
Digital (42, 108, 132)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 37, 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 (5, 71, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- digital (4, 37, 64)-net over F27, using
(108−66, 108, 224)-Net in Base 27 — Constructive
(42, 108, 224)-net in base 27, using
- t-expansion [i] based on (40, 108, 224)-net in base 27, using
- base change [i] based on digital (13, 81, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- base change [i] based on digital (13, 81, 224)-net over F81, using
(108−66, 108, 280)-Net over F27 — Digital
Digital (42, 108, 280)-net over F27, using
- net from sequence [i] based on digital (42, 279)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 42 and N(F) ≥ 280, using
(108−66, 108, 298)-Net in Base 27
(42, 108, 298)-net in base 27, using
- t-expansion [i] based on (39, 108, 298)-net in base 27, using
- base change [i] based on digital (12, 81, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- base change [i] based on digital (12, 81, 298)-net over F81, using
(108−66, 108, 24464)-Net in Base 27 — Upper bound on s
There is no (42, 108, 24465)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 38684 617157 329616 600621 983368 693652 531690 820075 598661 740881 144457 864746 782580 825424 884404 192402 751528 017918 718640 120254 413524 629459 519678 955664 561301 276475 > 27108 [i]