Best Known (27, 27+42, s)-Nets in Base 27
(27, 27+42, 114)-Net over F27 — Constructive and digital
Digital (27, 69, 114)-net over F27, using
- t-expansion [i] based on digital (23, 69, 114)-net over F27, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 23 and N(F) ≥ 114, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
(27, 27+42, 172)-Net in Base 27 — Constructive
(27, 69, 172)-net in base 27, using
- 11 times m-reduction [i] based on (27, 80, 172)-net in base 27, using
- base change [i] based on digital (7, 60, 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, 60, 172)-net over F81, using
(27, 27+42, 208)-Net over F27 — Digital
Digital (27, 69, 208)-net over F27, using
- t-expansion [i] based on digital (24, 69, 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
(27, 27+42, 244)-Net in Base 27
(27, 69, 244)-net in base 27, using
- 3 times m-reduction [i] based on (27, 72, 244)-net in base 27, using
- base change [i] based on digital (9, 54, 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, 54, 244)-net over F81, using
(27, 27+42, 16838)-Net in Base 27 — Upper bound on s
There is no (27, 69, 16839)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 581 553211 502640 274214 634096 368154 409698 789232 551850 545398 718296 723812 653643 906323 140857 635444 186735 > 2769 [i]