MinT - Best Known (136−63, 136, s)-Nets in Base 9

Best Known (136−63, 136, s)-Nets in Base 9

(136−63, 136, 320)-Net over F₉ — Constructive and digital

Digital (73, 136, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 68, 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]

(136−63, 136, 354)-Net over F₉ — Digital

Digital (73, 136, 354)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−63, 136, 22189)-Net in Base 9 — Upper bound on s

There is no (73, 136, 22190)-net in base 9, because

1 times m-reduction [i] would yield (73, 135, 22190)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 665 408438 289198 457888 020594 967338 654966 839381 891633 670547 347613 580077 099337 965313 546474 068986 748644 441067 413582 036710 481000 106705 > 9¹³⁵ [i]