MinT - Best Known (77, 77+47, s)-Nets in Base 4

Best Known (77, 77+47, s)-Nets in Base 4

(77, 77+47, 130)-Net over F₄ — Constructive and digital

Digital (77, 124, 130)-net over F₄, using

18 times m-reduction [i] based on digital (77, 142, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 71, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(77, 77+47, 234)-Net over F₄ — Digital

Digital (77, 124, 234)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+47, 5193)-Net in Base 4 — Upper bound on s

There is no (77, 124, 5194)-net in base 4, because

1 times m-reduction [i] would yield (77, 123, 5194)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 113 142049 633715 315776 134887 399817 931258 610153 185708 536002 492773 738325 122768 > 4¹²³ [i]