Best Known (28, 28+42, s)-Nets in Base 27
(28, 28+42, 116)-Net over F27 — Constructive and digital
Digital (28, 70, 116)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (3, 24, 52)-net over F27, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- digital (4, 46, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (3, 24, 52)-net over F27, using
(28, 28+42, 172)-Net in Base 27 — Constructive
(28, 70, 172)-net in base 27, using
- 14 times m-reduction [i] based on (28, 84, 172)-net in base 27, using
- base change [i] based on digital (7, 63, 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, 63, 172)-net over F81, using
(28, 28+42, 208)-Net over F27 — Digital
Digital (28, 70, 208)-net over F27, using
- t-expansion [i] based on digital (24, 70, 208)-net over F27, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 24 and N(F) ≥ 208, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
(28, 28+42, 244)-Net in Base 27
(28, 70, 244)-net in base 27, using
- 6 times m-reduction [i] based on (28, 76, 244)-net in base 27, using
- base change [i] based on digital (9, 57, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- base change [i] based on digital (9, 57, 244)-net over F81, using
(28, 28+42, 19701)-Net in Base 27 — Upper bound on s
There is no (28, 70, 19702)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 15696 902387 464974 572629 370531 005351 950701 983022 722118 659901 562355 729081 740182 207096 857565 527215 237813 > 2770 [i]