MinT - Best Known (68, 68+65, s)-Nets in Base 9

Best Known (68, 68+65, s)-Nets in Base 9

(68, 68+65, 200)-Net over F₉ — Constructive and digital

Digital (68, 133, 200)-net over F₉, using

1 times m-reduction [i] based on digital (68, 134, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 67, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(68, 68+65, 276)-Net over F₉ — Digital

Digital (68, 133, 276)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+65, 13785)-Net in Base 9 — Upper bound on s

There is no (68, 133, 13786)-net in base 9, because

1 times m-reduction [i] would yield (68, 132, 13786)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 912784 247839 179167 203227 879204 287362 264954 158548 032849 816964 584643 245925 534852 058308 269727 909982 399001 405282 417684 417711 169025 > 9¹³² [i]