MinT - Best Known (77, 77+37, s)-Nets in Base 4

Best Known (77, 77+37, s)-Nets in Base 4

(77, 77+37, 240)-Net over F₄ — Constructive and digital

Digital (77, 114, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 38, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(77, 77+37, 384)-Net over F₄ — Digital

Digital (77, 114, 384)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+37, 15142)-Net in Base 4 — Upper bound on s

There is no (77, 114, 15143)-net in base 4, because

1 times m-reduction [i] would yield (77, 113, 15143)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 107 928260 803064 534924 991466 385789 661349 558493 917641 075093 126641 252770 > 4¹¹³ [i]