MinT - Best Known (111−45, 111, s)-Nets in Base 4

Best Known (111−45, 111, s)-Nets in Base 4

(111−45, 111, 130)-Net over F₄ — Constructive and digital

Digital (66, 111, 130)-net over F₄, using

9 times m-reduction [i] based on digital (66, 120, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 60, 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]

(111−45, 111, 171)-Net over F₄ — Digital

Digital (66, 111, 171)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(111−45, 111, 3072)-Net in Base 4 — Upper bound on s

There is no (66, 111, 3073)-net in base 4, because

1 times m-reduction [i] would yield (66, 110, 3073)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 688268 389416 241958 166841 854841 102070 837521 271185 389194 123335 945728 > 4¹¹⁰ [i]