MinT - Best Known (57, 57+24, s)-Nets in Base 4

Best Known (57, 57+24, s)-Nets in Base 4

(57, 57+24, 312)-Net over F₄ — Constructive and digital

Digital (57, 81, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 27, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(57, 57+24, 426)-Net over F₄ — Digital

Digital (57, 81, 426)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+24, 20414)-Net in Base 4 — Upper bound on s

There is no (57, 81, 20415)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 5 847023 715318 513843 081408 362056 794254 351128 302373 > 4⁸¹ [i]