MinT - Best Known (44, 88, s)-Nets in Base 9

Best Known (44, 88, s)-Nets in Base 9

(44, 88, 164)-Net over F₉ — Constructive and digital

Digital (44, 88, 164)-net over F₉, using

trace code for nets [i] based on digital (0, 44, 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]

(44, 88, 179)-Net over F₉ — Digital

Digital (44, 88, 179)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(44, 88, 7412)-Net in Base 9 — Upper bound on s

There is no (44, 88, 7413)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 942181 237916 047856 404456 671802 116016 971593 004450 146095 392962 684760 984075 619734 399153 > 9⁸⁸ [i]