MinT - Best Known (111, 111+40, s)-Nets in Base 4

Best Known (111, 111+40, s)-Nets in Base 4

(111, 111+40, 531)-Net over F₄ — Constructive and digital

Digital (111, 151, 531)-net over F₄, using

5 times m-reduction [i] based on digital (111, 156, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 52, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(111, 111+40, 1119)-Net over F₄ — Digital

Digital (111, 151, 1119)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+40, 97199)-Net in Base 4 — Upper bound on s

There is no (111, 151, 97200)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 148360 458425 218598 060128 839829 723014 682615 385376 754308 952654 155384 594485 300369 415204 221786 > 4¹⁵¹ [i]