MinT - Best Known (61−27, 61, s)-Nets in Base 4

Best Known (61−27, 61, s)-Nets in Base 4

(61−27, 61, 76)-Net over F₄ — Constructive and digital

Digital (34, 61, 76)-net over F₄, using

1 times m-reduction [i] based on digital (34, 62, 76)-net over F₄, using
- trace code for nets [i] based on digital (3, 31, 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]

(61−27, 61, 82)-Net over F₄ — Digital

Digital (34, 61, 82)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(61−27, 61, 1124)-Net in Base 4 — Upper bound on s

There is no (34, 61, 1125)-net in base 4, because

1 times m-reduction [i] would yield (34, 60, 1125)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 332656 893519 815179 105741 765975 972176 > 4⁶⁰ [i]