MinT - Best Known (55, 105, s)-Nets in Base 9

Best Known (55, 105, s)-Nets in Base 9

(55, 105, 232)-Net over F₉ — Constructive and digital

Digital (55, 105, 232)-net over F₉, using

1 times m-reduction [i] based on digital (55, 106, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 53, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(55, 105, 253)-Net over F₉ — Digital

Digital (55, 105, 253)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 105, 12937)-Net in Base 9 — Upper bound on s

There is no (55, 105, 12938)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15702 308286 152488 166002 162883 409843 060668 280865 066628 081722 883470 026790 617021 164470 206115 834491 590865 > 9¹⁰⁵ [i]