MinT - Best Known (145−59, 145, s)-Nets in Base 9

Best Known (145−59, 145, s)-Nets in Base 9

(145−59, 145, 448)-Net over F₉ — Constructive and digital

Digital (86, 145, 448)-net over F₉, using

1 times m-reduction [i] based on digital (86, 146, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 73, 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]

(145−59, 145, 681)-Net over F₉ — Digital

Digital (86, 145, 681)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−59, 145, 79844)-Net in Base 9 — Upper bound on s

There is no (86, 145, 79845)-net in base 9, because

1 times m-reduction [i] would yield (86, 144, 79845)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 257652 562796 362526 008569 956520 213897 048570 866996 378828 553517 998959 909450 631380 968238 889251 254022 106636 096067 044969 693967 455924 960599 954953 > 9¹⁴⁴ [i]