Best Known (77−41, 77, s)-Nets in Base 27
(77−41, 77, 170)-Net over F27 — Constructive and digital
Digital (36, 77, 170)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 27, 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 (9, 50, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- digital (7, 27, 82)-net over F27, using
(77−41, 77, 348)-Net over F27 — Digital
Digital (36, 77, 348)-net over F27, using
(77−41, 77, 370)-Net in Base 27 — Constructive
(36, 77, 370)-net in base 27, using
- 3 times m-reduction [i] based on (36, 80, 370)-net in base 27, using
- base change [i] based on digital (16, 60, 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, 60, 370)-net over F81, using
(77−41, 77, 87793)-Net in Base 27 — Upper bound on s
There is no (36, 77, 87794)-net in base 27, because
- 1 times m-reduction [i] would yield (36, 76, 87794)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 6 076520 538139 679570 032005 222664 623074 617328 567287 746509 125195 479863 818725 372847 933811 459799 664017 031157 638857 > 2776 [i]