MinT - Best Known (55, 55+49, s)-Nets in Base 4

Best Known (55, 55+49, s)-Nets in Base 4

(55, 55+49, 76)-Net over F₄ — Constructive and digital

Digital (55, 104, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 52, 38)-net over F₁₆, using
- net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]

(55, 55+49, 100)-Net over F₄ — Digital

Digital (55, 104, 100)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+49, 1233)-Net in Base 4 — Upper bound on s

There is no (55, 104, 1234)-net in base 4, because

1 times m-reduction [i] would yield (55, 103, 1234)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 102 854572 767784 548923 508444 465710 260007 697688 282619 423982 767416 > 4¹⁰³ [i]