MinT - Best Known (113−51, 113, s)-Nets in Base 4

Best Known (113−51, 113, s)-Nets in Base 4

(113−51, 113, 98)-Net over F₄ — Constructive and digital

Digital (62, 113, 98)-net over F₄, using

1 times m-reduction [i] based on digital (62, 114, 98)-net over F₄, using
- trace code for nets [i] based on digital (5, 57, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]

(113−51, 113, 122)-Net over F₄ — Digital

Digital (62, 113, 122)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(113−51, 113, 1669)-Net in Base 4 — Upper bound on s

There is no (62, 113, 1670)-net in base 4, because

1 times m-reduction [i] would yield (62, 112, 1670)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 27 295613 611020 678063 538198 844140 834038 398420 038619 272173 308535 790672 > 4¹¹² [i]