MinT - Best Known (57, 57+37, s)-Nets in Base 4

Best Known (57, 57+37, s)-Nets in Base 4

(57, 57+37, 130)-Net over F₄ — Constructive and digital

Digital (57, 94, 130)-net over F₄, using

8 times m-reduction [i] based on digital (57, 102, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 51, 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]

(57, 57+37, 165)-Net over F₄ — Digital

Digital (57, 94, 165)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+37, 3233)-Net in Base 4 — Upper bound on s

There is no (57, 94, 3234)-net in base 4, because

1 times m-reduction [i] would yield (57, 93, 3234)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 98 191306 389445 592673 848086 145060 063064 824585 038578 564256 > 4⁹³ [i]