MinT - Best Known (61, 61+55, s)-Nets in Base 4

Best Known (61, 61+55, s)-Nets in Base 4

(61, 61+55, 76)-Net over F₄ — Constructive and digital

Digital (61, 116, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 58, 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]

(61, 61+55, 107)-Net over F₄ — Digital

Digital (61, 116, 107)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+55, 1313)-Net in Base 4 — Upper bound on s

There is no (61, 116, 1314)-net in base 4, because

1 times m-reduction [i] would yield (61, 115, 1314)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1741 211943 527742 880485 336122 282395 445895 700648 593979 155887 968625 266000 > 4¹¹⁵ [i]