Best Known (138−71, 138, s)-Nets in Base 9
(138−71, 138, 165)-Net over F9 — Constructive and digital
Digital (67, 138, 165)-net over F9, using
- t-expansion [i] based on digital (64, 138, 165)-net over F9, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
(138−71, 138, 228)-Net over F9 — Digital
Digital (67, 138, 228)-net over F9, using
(138−71, 138, 9426)-Net in Base 9 — Upper bound on s
There is no (67, 138, 9427)-net in base 9, because
- 1 times m-reduction [i] would yield (67, 137, 9427)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 53875 740215 112376 960485 872142 330802 106894 383120 677984 625829 400606 192108 250617 029355 243533 172632 702552 939215 524072 739366 988326 537545 > 9137 [i]