MinT - Best Known (137−63, 137, s)-Nets in Base 9

Best Known (137−63, 137, s)-Nets in Base 9

(137−63, 137, 320)-Net over F₉ — Constructive and digital

Digital (74, 137, 320)-net over F₉, using

1 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]

(137−63, 137, 367)-Net over F₉ — Digital

Digital (74, 137, 367)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−63, 137, 23820)-Net in Base 9 — Upper bound on s

There is no (74, 137, 23821)-net in base 9, because

1 times m-reduction [i] would yield (74, 136, 23821)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 5986 714175 822941 031693 842991 562633 681497 884643 330308 434526 232889 761046 022332 150035 331434 008573 172858 941635 941310 575824 927279 442265 > 9¹³⁶ [i]