MinT - Best Known (56, 56+49, s)-Nets in Base 4

Best Known (56, 56+49, s)-Nets in Base 4

(56, 56+49, 76)-Net over F₄ — Constructive and digital

Digital (56, 105, 76)-net over F₄, using

1 times m-reduction [i] based on digital (56, 106, 76)-net over F₄, using
- trace code for nets [i] based on digital (3, 53, 38)-net over F₁₆, using
  - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(56, 56+49, 104)-Net over F₄ — Digital

Digital (56, 105, 104)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+49, 1308)-Net in Base 4 — Upper bound on s

There is no (56, 105, 1309)-net in base 4, because

1 times m-reduction [i] would yield (56, 104, 1309)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 414 975443 416056 481525 828873 766418 359803 849819 614835 066692 405451 > 4¹⁰⁴ [i]