MinT - Best Known (62, 62+49, s)-Nets in Base 4

Best Known (62, 62+49, s)-Nets in Base 4

(62, 62+49, 130)-Net over F₄ — Constructive and digital

Digital (62, 111, 130)-net over F₄, using

1 times m-reduction [i] based on digital (62, 112, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 56, 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]

(62, 62+49, 1858)-Net in Base 4 — Upper bound on s

There is no (62, 111, 1859)-net in base 4, because

1 times m-reduction [i] would yield (62, 110, 1859)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 695283 925572 354137 028192 942265 544012 004396 399012 670757 099382 025416 > 4¹¹⁰ [i]