MinT - Best Known (171−55, 171, s)-Nets in Base 4

Best Known (171−55, 171, s)-Nets in Base 4

(171−55, 171, 240)-Net over F₄ — Constructive and digital

Digital (116, 171, 240)-net over F₄, using

t-expansion [i] based on digital (115, 171, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 57, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(171−55, 171, 550)-Net over F₄ — Digital

Digital (116, 171, 550)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−55, 171, 22470)-Net in Base 4 — Upper bound on s

There is no (116, 171, 22471)-net in base 4, because

1 times m-reduction [i] would yield (116, 170, 22471)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 241641 291696 195242 077913 867347 292071 781735 632483 115772 824776 688077 159903 342583 677645 620897 982469 046848 > 4¹⁷⁰ [i]