MinT - Best Known (127, 189, s)-Nets in Base 4

Best Known (127, 189, s)-Nets in Base 4

(127, 189, 240)-Net over F₄ — Constructive and digital

Digital (127, 189, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 63, 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]

(127, 189, 556)-Net over F₄ — Digital

Digital (127, 189, 556)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 189, 19362)-Net in Base 4 — Upper bound on s

There is no (127, 189, 19363)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 615861 574993 876243 144878 154843 176569 162025 069781 501949 365017 364207 676927 699742 426754 004874 349445 405694 455859 518080 > 4¹⁸⁹ [i]