MinT - Best Known (100−41, 100, s)-Nets in Base 9

Best Known (100−41, 100, s)-Nets in Base 9

(100−41, 100, 344)-Net over F₉ — Constructive and digital

Digital (59, 100, 344)-net over F₉, using

4 times m-reduction [i] based on digital (59, 104, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 52, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(100−41, 100, 489)-Net over F₉ — Digital

Digital (59, 100, 489)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(100−41, 100, 54906)-Net in Base 9 — Upper bound on s

There is no (59, 100, 54907)-net in base 9, because

1 times m-reduction [i] would yield (59, 99, 54907)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29520 751752 184615 357970 572091 175833 650994 105964 805166 534598 745310 980182 577917 304148 729068 226529 > 9⁹⁹ [i]