MinT - Best Known (64, 64+52, s)-Nets in Base 4

Best Known (64, 64+52, s)-Nets in Base 4

(64, 64+52, 130)-Net over F₄ — Constructive and digital

Digital (64, 116, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 58, 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]

(64, 64+52, 1686)-Net in Base 4 — Upper bound on s

There is no (64, 116, 1687)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6992 884258 548714 729521 330734 933339 375513 044930 252743 753499 798647 076880 > 4¹¹⁶ [i]