MinT - Best Known (135−61, 135, s)-Nets in Base 9

Best Known (135−61, 135, s)-Nets in Base 9

(135−61, 135, 320)-Net over F₉ — Constructive and digital

Digital (74, 135, 320)-net over F₉, using

3 times m-reduction [i] based on digital (74, 138, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 69, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(135−61, 135, 392)-Net over F₉ — Digital

Digital (74, 135, 392)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−61, 135, 27522)-Net in Base 9 — Upper bound on s

There is no (74, 135, 27523)-net in base 9, because

1 times m-reduction [i] would yield (74, 134, 27523)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 73 883466 713249 176610 270939 508102 060404 310774 157084 898170 616497 022920 743981 970679 321327 690696 576184 725123 518242 607141 522501 986129 > 9¹³⁴ [i]