Best Known (57−35, 57, s)-Nets in Base 27
(57−35, 57, 112)-Net over F27 — Constructive and digital
Digital (22, 57, 112)-net over F27, using
- net from sequence [i] based on digital (22, 111)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 22 and N(F) ≥ 112, using
(57−35, 57, 163)-Net over F27 — Digital
Digital (22, 57, 163)-net over F27, using
- t-expansion [i] based on digital (21, 57, 163)-net over F27, using
- net from sequence [i] based on digital (21, 162)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 21 and N(F) ≥ 163, using
- net from sequence [i] based on digital (21, 162)-sequence over F27, using
(57−35, 57, 172)-Net in Base 27 — Constructive
(22, 57, 172)-net in base 27, using
- 3 times m-reduction [i] based on (22, 60, 172)-net in base 27, using
- base change [i] based on digital (7, 45, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 45, 172)-net over F81, using
(57−35, 57, 190)-Net in Base 27
(22, 57, 190)-net in base 27, using
- 7 times m-reduction [i] based on (22, 64, 190)-net in base 27, using
- base change [i] based on digital (6, 48, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- base change [i] based on digital (6, 48, 190)-net over F81, using
(57−35, 57, 14314)-Net in Base 27 — Upper bound on s
There is no (22, 57, 14315)-net in base 27, because
- 1 times m-reduction [i] would yield (22, 56, 14315)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 143 348338 311696 019793 531489 641353 026904 581218 976751 013131 286774 535741 438050 289343 > 2756 [i]