Best Known (55, 55+34, s)-Nets in Base 9
(55, 55+34, 344)-Net over F9 — Constructive and digital
Digital (55, 89, 344)-net over F9, using
- 7 times m-reduction [i] based on digital (55, 96, 344)-net over F9, using
- trace code for nets [i] based on digital (7, 48, 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
- trace code for nets [i] based on digital (7, 48, 172)-net over F81, using
(55, 55+34, 633)-Net over F9 — Digital
Digital (55, 89, 633)-net over F9, using
(55, 55+34, 88827)-Net in Base 9 — Upper bound on s
There is no (55, 89, 88828)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 8 465463 857167 723733 401317 613015 611392 518142 521449 756871 944276 149200 734392 969289 507297 > 989 [i]