MinT - Best Known (236−67, 236, s)-Nets in Base 4

Best Known (236−67, 236, s)-Nets in Base 4

(236−67, 236, 531)-Net over F₄ — Constructive and digital

Digital (169, 236, 531)-net over F₄, using

7 times m-reduction [i] based on digital (169, 243, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 81, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(236−67, 236, 1207)-Net over F₄ — Digital

Digital (169, 236, 1207)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−67, 236, 85014)-Net in Base 4 — Upper bound on s

There is no (169, 236, 85015)-net in base 4, because

1 times m-reduction [i] would yield (169, 235, 85015)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3049 435966 955715 052603 171666 148270 325825 585063 195033 145783 798357 961713 476455 009501 150243 636574 255111 347320 954504 912416 414396 348175 983568 148800 > 4²³⁵ [i]