MinT - Best Known (57, 57+27, s)-Nets in Base 4

Best Known (57, 57+27, s)-Nets in Base 4

(57, 57+27, 240)-Net over F₄ — Constructive and digital

Digital (57, 84, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 28, 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]

(57, 57+27, 321)-Net over F₄ — Digital

Digital (57, 84, 321)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+27, 13178)-Net in Base 4 — Upper bound on s

There is no (57, 84, 13179)-net in base 4, because

1 times m-reduction [i] would yield (57, 83, 13179)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 93 581848 415007 636871 425852 322953 088289 694290 944072 > 4⁸³ [i]