Best Known (109−51, 109, s)-Nets in Base 27
(109−51, 109, 216)-Net over F27 — Constructive and digital
Digital (58, 109, 216)-net over F27, using
- generalized (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, 31, 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 (6, 57, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (4, 21, 64)-net over F27, using
(109−51, 109, 370)-Net in Base 27 — Constructive
(58, 109, 370)-net in base 27, using
- 271 times duplication [i] based on (57, 108, 370)-net in base 27, using
- t-expansion [i] based on (43, 108, 370)-net in base 27, using
- base change [i] based on digital (16, 81, 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, 81, 370)-net over F81, using
- t-expansion [i] based on (43, 108, 370)-net in base 27, using
(109−51, 109, 1014)-Net over F27 — Digital
Digital (58, 109, 1014)-net over F27, using
(109−51, 109, 597220)-Net in Base 27 — Upper bound on s
There is no (58, 109, 597221)-net in base 27, because
- 1 times m-reduction [i] would yield (58, 108, 597221)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 38663 433062 920988 831495 356227 864152 608310 631596 054012 447186 531608 327444 368456 103229 452822 335833 144397 482723 555481 865073 885362 713629 520739 405031 041833 162915 > 27108 [i]