MinT - Best Known (117−55, 117, s)-Nets in Base 9

Best Known (117−55, 117, s)-Nets in Base 9

(117−55, 117, 232)-Net over F₉ — Constructive and digital

Digital (62, 117, 232)-net over F₉, using

3 times m-reduction [i] based on digital (62, 120, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 60, 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]

(117−55, 117, 292)-Net over F₉ — Digital

Digital (62, 117, 292)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−55, 117, 17163)-Net in Base 9 — Upper bound on s

There is no (62, 117, 17164)-net in base 9, because

1 times m-reduction [i] would yield (62, 116, 17164)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 492 407826 646805 310722 415541 514522 388056 392407 878997 468670 278812 259054 833277 614576 439960 522681 672069 409599 932065 > 9¹¹⁶ [i]