Best Known (73, 73+61, s)-Nets in Base 9
(73, 73+61, 320)-Net over F9 — Constructive and digital
Digital (73, 134, 320)-net over F9, using
- 2 times m-reduction [i] based on digital (73, 136, 320)-net over F9, using
- trace code for nets [i] based on digital (5, 68, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- trace code for nets [i] based on digital (5, 68, 160)-net over F81, using
(73, 73+61, 380)-Net over F9 — Digital
Digital (73, 134, 380)-net over F9, using
- trace code for nets [i] based on digital (6, 67, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
(73, 73+61, 25577)-Net in Base 9 — Upper bound on s
There is no (73, 134, 25578)-net in base 9, because
- 1 times m-reduction [i] would yield (73, 133, 25578)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 8 209711 068527 622932 192940 139367 975984 228558 998030 400360 252546 841804 724014 086401 844443 354965 383818 742891 275385 532277 646040 882337 > 9133 [i]