Best Known (80−34, 80, s)-Nets in Base 27
(80−34, 80, 228)-Net over F27 — Constructive and digital
Digital (46, 80, 228)-net over F27, using
- 1 times m-reduction [i] based on digital (46, 81, 228)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 17, 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, 23, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 41, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 17, 76)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(80−34, 80, 370)-Net in Base 27 — Constructive
(46, 80, 370)-net in base 27, using
- t-expansion [i] based on (43, 80, 370)-net in base 27, using
- 28 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
- 28 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(80−34, 80, 1511)-Net over F27 — Digital
Digital (46, 80, 1511)-net over F27, using
(80−34, 80, 1502445)-Net in Base 27 — Upper bound on s
There is no (46, 80, 1502446)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 3 229250 576728 617620 722572 045407 758930 049756 074245 617929 070439 533831 678509 362368 564341 739436 604330 495213 115771 918349 > 2780 [i]