MinT - Best Known (68, 68+53, s)-Nets in Base 9

Best Known (68, 68+53, s)-Nets in Base 9

(68, 68+53, 344)-Net over F₉ — Constructive and digital

Digital (68, 121, 344)-net over F₉, using

1 times m-reduction [i] based on digital (68, 122, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 61, 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]

(68, 68+53, 412)-Net over F₉ — Digital

Digital (68, 121, 412)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+53, 33434)-Net in Base 9 — Upper bound on s

There is no (68, 121, 33435)-net in base 9, because

1 times m-reduction [i] would yield (68, 120, 33435)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 230518 542328 302900 881741 046688 735082 000304 196887 071883 646804 249591 604218 975964 044760 366142 591867 255520 675692 201585 > 9¹²⁰ [i]