MinT - Best Known (55, 55+43, s)-Nets in Base 4

Best Known (55, 55+43, s)-Nets in Base 4

(55, 55+43, 130)-Net over F₄ — Constructive and digital

Digital (55, 98, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 49, 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]

(55, 55+43, 1730)-Net in Base 4 — Upper bound on s

There is no (55, 98, 1731)-net in base 4, because

1 times m-reduction [i] would yield (55, 97, 1731)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 25365 345039 586015 665113 309174 184545 737997 326492 507359 304096 > 4⁹⁷ [i]