MinT - Best Known (45, 78, s)-Nets in Base 4

Best Known (45, 78, s)-Nets in Base 4

(45, 78, 130)-Net over F₄ — Constructive and digital

Digital (45, 78, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 39, 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]

(45, 78, 1777)-Net in Base 4 — Upper bound on s

There is no (45, 78, 1778)-net in base 4, because

1 times m-reduction [i] would yield (45, 77, 1778)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 23017 868808 721081 273072 476778 925892 870291 389155 > 4⁷⁷ [i]