MinT - Best Known (133−63, 133, s)-Nets in Base 9

Best Known (133−63, 133, s)-Nets in Base 9

(133−63, 133, 232)-Net over F₉ — Constructive and digital

Digital (70, 133, 232)-net over F₉, using

3 times m-reduction [i] based on digital (70, 136, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 68, 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]

(133−63, 133, 316)-Net over F₉ — Digital

Digital (70, 133, 316)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−63, 133, 17935)-Net in Base 9 — Upper bound on s

There is no (70, 133, 17936)-net in base 9, because

1 times m-reduction [i] would yield (70, 132, 17936)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 912887 779196 387242 813162 031417 895077 249622 150232 507161 699177 547714 790142 395636 607204 404250 588831 779739 500898 078642 369289 666945 > 9¹³² [i]