MinT - Best Known (62, 62+55, s)-Nets in Base 4

Best Known (62, 62+55, s)-Nets in Base 4

(62, 62+55, 76)-Net over F₄ — Constructive and digital

Digital (62, 117, 76)-net over F₄, using

1 times m-reduction [i] based on digital (62, 118, 76)-net over F₄, using
- trace code for nets [i] based on digital (3, 59, 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]

(62, 62+55, 111)-Net over F₄ — Digital

Digital (62, 117, 111)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+55, 1383)-Net in Base 4 — Upper bound on s

There is no (62, 117, 1384)-net in base 4, because

1 times m-reduction [i] would yield (62, 116, 1384)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6915 097894 572672 356985 998460 990365 535184 300272 160355 351277 564960 316540 > 4¹¹⁶ [i]