Best Known (53, 53+42, s)-Nets in Base 27
(53, 53+42, 228)-Net over F27 — Constructive and digital
Digital (53, 95, 228)-net over F27, using
- 1 times m-reduction [i] based on digital (53, 96, 228)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 20, 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, 27, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 49, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 20, 76)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(53, 53+42, 370)-Net in Base 27 — Constructive
(53, 95, 370)-net in base 27, using
- t-expansion [i] based on (43, 95, 370)-net in base 27, using
- 13 times m-reduction [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
- 13 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(53, 53+42, 1307)-Net over F27 — Digital
Digital (53, 95, 1307)-net over F27, using
(53, 53+42, 997083)-Net in Base 27 — Upper bound on s
There is no (53, 95, 997084)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 9540 298082 247949 046902 847956 825746 819600 914490 608056 765498 836454 580688 350559 245547 339685 869990 175612 457660 510984 247007 366481 652208 912185 > 2795 [i]