MinT - Best Known (57, 57+47, s)-Nets in Base 4

Best Known (57, 57+47, s)-Nets in Base 4

(57, 57+47, 98)-Net over F₄ — Constructive and digital

Digital (57, 104, 98)-net over F₄, using

trace code for nets [i] based on digital (5, 52, 49)-net over F₁₆, using
- net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
    - a function field by SÃ©mirat [i]

(57, 57+47, 114)-Net over F₄ — Digital

Digital (57, 104, 114)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+47, 1542)-Net in Base 4 — Upper bound on s

There is no (57, 104, 1543)-net in base 4, because

1 times m-reduction [i] would yield (57, 103, 1543)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 103 104819 590734 461730 303646 876490 584688 906644 017349 891562 659200 > 4¹⁰³ [i]