Best Known (39, 39+42, s)-Nets in Base 27
(39, 39+42, 178)-Net over F27 — Constructive and digital
Digital (39, 81, 178)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (8, 29, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- digital (10, 52, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- digital (8, 29, 84)-net over F27, using
(39, 39+42, 370)-Net in Base 27 — Constructive
(39, 81, 370)-net in base 27, using
- 11 times m-reduction [i] based on (39, 92, 370)-net in base 27, using
- base change [i] based on digital (16, 69, 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, 69, 370)-net over F81, using
(39, 39+42, 425)-Net over F27 — Digital
Digital (39, 81, 425)-net over F27, using
(39, 39+42, 110777)-Net in Base 27 — Upper bound on s
There is no (39, 81, 110778)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 87 198704 943386 507114 671322 748974 619095 895658 105001 025993 086433 220629 311124 045047 090707 858815 393864 315583 814107 301789 > 2781 [i]