MinT - Best Known (53, 53+41, s)-Nets in Base 4

Best Known (53, 53+41, s)-Nets in Base 4

(53, 53+41, 130)-Net over F₄ — Constructive and digital

Digital (53, 94, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 47, 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]

(53, 53+41, 1728)-Net in Base 4 — Upper bound on s

There is no (53, 94, 1729)-net in base 4, because

1 times m-reduction [i] would yield (53, 93, 1729)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 98 344883 886970 040452 177205 827629 429299 739951 365251 435216 > 4⁹³ [i]