MinT - Best Known (111−41, 111, s)-Nets in Base 4

Best Known (111−41, 111, s)-Nets in Base 4

(111−41, 111, 130)-Net over F₄ — Constructive and digital

Digital (70, 111, 130)-net over F₄, using

17 times m-reduction [i] based on digital (70, 128, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 64, 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]

(111−41, 111, 233)-Net over F₄ — Digital

Digital (70, 111, 233)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(111−41, 111, 5652)-Net in Base 4 — Upper bound on s

There is no (70, 111, 5653)-net in base 4, because

1 times m-reduction [i] would yield (70, 110, 5653)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 685224 254817 061765 149905 026299 215046 079556 344637 188023 102874 691121 > 4¹¹⁰ [i]