MinT - Best Known (57, 57+35, s)-Nets in Base 4

Best Known (57, 57+35, s)-Nets in Base 4

(57, 57+35, 130)-Net over F₄ — Constructive and digital

Digital (57, 92, 130)-net over F₄, using

10 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+35, 182)-Net over F₄ — Digital

Digital (57, 92, 182)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+35, 3982)-Net in Base 4 — Upper bound on s

There is no (57, 92, 3983)-net in base 4, because

1 times m-reduction [i] would yield (57, 91, 3983)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6 149278 618183 023135 347081 195812 654191 573211 207386 993424 > 4⁹¹ [i]