MinT - Best Known (52, 52+44, s)-Nets in Base 4

Best Known (52, 52+44, s)-Nets in Base 4

(52, 52+44, 90)-Net over F₄ — Constructive and digital

Digital (52, 96, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 48, 45)-net over F₁₆, using
- net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
    - a function field by GarcÃa and Quoos [i]

(52, 52+44, 102)-Net over F₄ — Digital

Digital (52, 96, 102)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+44, 1261)-Net in Base 4 — Upper bound on s

There is no (52, 96, 1262)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6346 948687 731503 739078 304123 034300 324122 803903 319856 975320 > 4⁹⁶ [i]