MinT - Best Known (146−67, 146, s)-Nets in Base 9

Best Known (146−67, 146, s)-Nets in Base 9

(146−67, 146, 320)-Net over F₉ — Constructive and digital

Digital (79, 146, 320)-net over F₉, using

2 times m-reduction [i] based on digital (79, 148, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 74, 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]

(146−67, 146, 392)-Net over F₉ — Digital

Digital (79, 146, 392)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−67, 146, 25633)-Net in Base 9 — Upper bound on s

There is no (79, 146, 25634)-net in base 9, because

1 times m-reduction [i] would yield (79, 145, 25634)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 319899 094652 695009 859682 041752 272701 240383 878048 058610 388405 774430 746805 628257 990040 468098 054165 125950 260879 124300 912968 965991 512624 598801 > 9¹⁴⁵ [i]