MinT - Best Known (102−47, 102, s)-Nets in Base 4

Best Known (102−47, 102, s)-Nets in Base 4

(102−47, 102, 90)-Net over F₄ — Constructive and digital

Digital (55, 102, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 51, 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]

(102−47, 102, 106)-Net over F₄ — Digital

Digital (55, 102, 106)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(102−47, 102, 1365)-Net in Base 4 — Upper bound on s

There is no (55, 102, 1366)-net in base 4, because

1 times m-reduction [i] would yield (55, 101, 1366)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 479466 749353 991454 873499 933182 591528 998006 694312 854313 507856 > 4¹⁰¹ [i]