Best Known (35, 35+60, s)-Nets in Base 27
(35, 35+60, 114)-Net over F27 — Constructive and digital
Digital (35, 95, 114)-net over F27, using
- t-expansion [i] based on digital (23, 95, 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
(35, 35+60, 172)-Net in Base 27 — Constructive
(35, 95, 172)-net in base 27, using
- t-expansion [i] based on (34, 95, 172)-net in base 27, using
- 13 times m-reduction [i] based on (34, 108, 172)-net in base 27, using
- base change [i] based on digital (7, 81, 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, 81, 172)-net over F81, using
- 13 times m-reduction [i] based on (34, 108, 172)-net in base 27, using
(35, 35+60, 220)-Net over F27 — Digital
Digital (35, 95, 220)-net over F27, using
- t-expansion [i] based on digital (33, 95, 220)-net over F27, using
- net from sequence [i] based on digital (33, 219)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 33 and N(F) ≥ 220, using
- net from sequence [i] based on digital (33, 219)-sequence over F27, using
(35, 35+60, 244)-Net in Base 27
(35, 95, 244)-net in base 27, using
- 9 times m-reduction [i] based on (35, 104, 244)-net in base 27, using
- base change [i] based on digital (9, 78, 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, 78, 244)-net over F81, using
(35, 35+60, 15777)-Net in Base 27 — Upper bound on s
There is no (35, 95, 15778)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 9550 276767 333461 599651 505174 838646 719801 427934 275614 755507 282143 572185 552338 309940 818360 763744 765809 089535 305504 712883 813867 038692 347181 > 2795 [i]