MinT - Best Known (107, 150, s)-Nets in Base 4

Best Known (107, 150, s)-Nets in Base 4

(107, 150, 531)-Net over F₄ — Constructive and digital

Digital (107, 150, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 50, 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]

(107, 150, 799)-Net over F₄ — Digital

Digital (107, 150, 799)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 150, 54074)-Net in Base 4 — Upper bound on s

There is no (107, 150, 54075)-net in base 4, because

1 times m-reduction [i] would yield (107, 149, 54075)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 509326 081574 041107 081249 444718 929575 972126 532709 919780 781294 798036 518043 669000 916530 040636 > 4¹⁴⁹ [i]