Best Known (52, 52+64, s)-Nets in Base 9
(52, 52+64, 102)-Net over F9 — Constructive and digital
Digital (52, 116, 102)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 35, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- digital (17, 81, 74)-net over F9, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- digital (3, 35, 28)-net over F9, using
(52, 52+64, 182)-Net over F9 — Digital
Digital (52, 116, 182)-net over F9, using
- t-expansion [i] based on digital (50, 116, 182)-net over F9, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 50 and N(F) ≥ 182, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
(52, 52+64, 4582)-Net in Base 9 — Upper bound on s
There is no (52, 116, 4583)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 494 806896 690001 503179 292754 530512 960844 886493 997847 876579 934313 955494 992178 680486 301828 232408 442632 841860 036353 > 9116 [i]