MinT - Best Known (33, 33+27, s)-Nets in Base 4

Best Known (33, 33+27, s)-Nets in Base 4

(33, 33+27, 76)-Net over F₄ — Constructive and digital

Digital (33, 60, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 30, 38)-net over F₁₆, using
- net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]

(33, 33+27, 77)-Net over F₄ — Digital

Digital (33, 60, 77)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(33, 33+27, 1009)-Net in Base 4 — Upper bound on s

There is no (33, 60, 1010)-net in base 4, because

1 times m-reduction [i] would yield (33, 59, 1010)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 332443 702806 641549 597693 552885 846620 > 4⁵⁹ [i]