MinT - Best Known (70−29, 70, s)-Nets in Base 4

Best Known (70−29, 70, s)-Nets in Base 4

(70−29, 70, 130)-Net over F₄ — Constructive and digital

Digital (41, 70, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 35, 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]

(70−29, 70, 1857)-Net in Base 4 — Upper bound on s

There is no (41, 70, 1858)-net in base 4, because

1 times m-reduction [i] would yield (41, 69, 1858)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 348559 820768 957423 246418 542877 003395 874400 > 4⁶⁹ [i]