MinT - Best Known (68, 68+39, s)-Nets in Base 9

Best Known (68, 68+39, s)-Nets in Base 9

(68, 68+39, 448)-Net over F₉ — Constructive and digital

Digital (68, 107, 448)-net over F₉, using

3 times m-reduction [i] based on digital (68, 110, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 55, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(68, 68+39, 932)-Net over F₉ — Digital

Digital (68, 107, 932)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+39, 208819)-Net in Base 9 — Upper bound on s

There is no (68, 107, 208820)-net in base 9, because

1 times m-reduction [i] would yield (68, 106, 208820)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 141167 374054 982437 140425 598287 022956 472176 578474 117338 122563 125576 457310 582088 285870 346863 059083 397217 > 9¹⁰⁶ [i]