Best Known (79−50, 79, s)-Nets in Base 27
(79−50, 79, 114)-Net over F27 — Constructive and digital
Digital (29, 79, 114)-net over F27, using
- t-expansion [i] based on digital (23, 79, 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
(79−50, 79, 172)-Net in Base 27 — Constructive
(29, 79, 172)-net in base 27, using
- 9 times m-reduction [i] based on (29, 88, 172)-net in base 27, using
- base change [i] based on digital (7, 66, 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, 66, 172)-net over F81, using
(79−50, 79, 208)-Net over F27 — Digital
Digital (29, 79, 208)-net over F27, using
- t-expansion [i] based on digital (24, 79, 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
(79−50, 79, 244)-Net in Base 27
(29, 79, 244)-net in base 27, using
- 1 times m-reduction [i] based on (29, 80, 244)-net in base 27, using
- base change [i] based on digital (9, 60, 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, 60, 244)-net over F81, using
(79−50, 79, 13041)-Net in Base 27 — Upper bound on s
There is no (29, 79, 13042)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 119694 864696 444902 290435 309625 893198 892579 421612 649244 255266 636629 895656 296371 270474 450553 709461 552227 870249 442853 > 2779 [i]