MinT - Best Known (160−47, 160, s)-Nets in Base 4

Best Known (160−47, 160, s)-Nets in Base 4

(160−47, 160, 384)-Net over F₄ — Constructive and digital

Digital (113, 160, 384)-net over F₄, using

2 times m-reduction [i] based on digital (113, 162, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 54, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(160−47, 160, 755)-Net over F₄ — Digital

Digital (113, 160, 755)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−47, 160, 45627)-Net in Base 4 — Upper bound on s

There is no (113, 160, 45628)-net in base 4, because

1 times m-reduction [i] would yield (113, 159, 45628)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 534198 136122 278701 088517 178858 935478 635717 228599 585218 557766 575483 014912 285623 467367 436068 264630 > 4¹⁵⁹ [i]