MinT - Best Known (123−59, 123, s)-Nets in Base 9

Best Known (123−59, 123, s)-Nets in Base 9

(123−59, 123, 232)-Net over F₉ — Constructive and digital

Digital (64, 123, 232)-net over F₉, using

1 times m-reduction [i] based on digital (64, 124, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 62, 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]

(123−59, 123, 280)-Net over F₉ — Digital

Digital (64, 123, 280)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−59, 123, 15063)-Net in Base 9 — Upper bound on s

There is no (64, 123, 15064)-net in base 9, because

1 times m-reduction [i] would yield (64, 122, 15064)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 261 855504 178679 934246 561574 183764 754301 303369 727410 501252 809159 518156 553992 750661 890714 388176 537341 613022 550461 306305 > 9¹²² [i]