MinT - Best Known (113−49, 113, s)-Nets in Base 9

Best Known (113−49, 113, s)-Nets in Base 9

(113−49, 113, 344)-Net over F₉ — Constructive and digital

Digital (64, 113, 344)-net over F₉, using

1 times m-reduction [i] based on digital (64, 114, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 57, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(113−49, 113, 409)-Net over F₉ — Digital

Digital (64, 113, 409)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(113−49, 113, 34771)-Net in Base 9 — Upper bound on s

There is no (64, 113, 34772)-net in base 9, because

1 times m-reduction [i] would yield (64, 112, 34772)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 75043 160414 929989 882711 038017 965275 669051 560596 201487 523621 852920 976088 458118 819068 272216 217469 101599 947009 > 9¹¹² [i]