MinT - Best Known (113−53, 113, s)-Nets in Base 9

Best Known (113−53, 113, s)-Nets in Base 9

(113−53, 113, 232)-Net over F₉ — Constructive and digital

Digital (60, 113, 232)-net over F₉, using

3 times m-reduction [i] based on digital (60, 116, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 58, 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]

(113−53, 113, 287)-Net over F₉ — Digital

Digital (60, 113, 287)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(113−53, 113, 16997)-Net in Base 9 — Upper bound on s

There is no (60, 113, 16998)-net in base 9, because

1 times m-reduction [i] would yield (60, 112, 16998)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 75079 086172 871385 007893 770952 131125 388840 093036 170227 940126 458045 634371 142443 103048 762323 698555 360691 562785 > 9¹¹² [i]