MinT - Best Known (61, 61+54, s)-Nets in Base 4

Best Known (61, 61+54, s)-Nets in Base 4

(61, 61+54, 76)-Net over F₄ — Constructive and digital

Digital (61, 115, 76)-net over F₄, using

1 times m-reduction [i] based on 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+54, 110)-Net over F₄ — Digital

Digital (61, 115, 110)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+54, 1313)-Net in Base 4 — Upper bound on s

There is no (61, 115, 1314)-net in base 4, because

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]