MinT - Best Known (68−34, 68, s)-Nets in Base 9

Best Known (68−34, 68, s)-Nets in Base 9

(68−34, 68, 164)-Net over F₉ — Constructive and digital

Digital (34, 68, 164)-net over F₉, using

trace code for nets [i] based on digital (0, 34, 82)-net over F₈₁, using
- net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
    - the rational function field F₈₁(x) [i]
  - Niederreiter sequence [i]

(68−34, 68, 5875)-Net in Base 9 — Upper bound on s

There is no (34, 68, 5876)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 77367 009000 307269 114331 183528 915690 636463 013753 441230 052559 844769 > 9⁶⁸ [i]