Best Known (80−50, 80, s)-Nets in Base 27
(80−50, 80, 114)-Net over F27 — Constructive and digital
Digital (30, 80, 114)-net over F27, using
- t-expansion [i] based on digital (23, 80, 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
(80−50, 80, 172)-Net in Base 27 — Constructive
(30, 80, 172)-net in base 27, using
- 12 times m-reduction [i] based on (30, 92, 172)-net in base 27, using
- base change [i] based on digital (7, 69, 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, 69, 172)-net over F81, using
(80−50, 80, 208)-Net over F27 — Digital
Digital (30, 80, 208)-net over F27, using
- t-expansion [i] based on digital (24, 80, 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
(80−50, 80, 244)-Net in Base 27
(30, 80, 244)-net in base 27, using
- 4 times m-reduction [i] based on (30, 84, 244)-net in base 27, using
- base change [i] based on digital (9, 63, 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, 63, 244)-net over F81, using
(80−50, 80, 14881)-Net in Base 27 — Upper bound on s
There is no (30, 80, 14882)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 3 233484 735497 028392 008125 728104 852074 186472 230760 061934 355833 706123 353764 155472 519497 601040 169096 786721 684089 668357 > 2780 [i]