MinT - Best Known (39, 66, s)-Nets in Base 4

Best Known (39, 66, s)-Nets in Base 4

(39, 66, 130)-Net over F₄ — Constructive and digital

Digital (39, 66, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 33, 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]

(39, 66, 1924)-Net in Base 4 — Upper bound on s

There is no (39, 66, 1925)-net in base 4, because

1 times m-reduction [i] would yield (39, 65, 1925)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1367 912914 398245 454054 634128 745014 024256 > 4⁶⁵ [i]