MinT - Best Known (112, 112+40, s)-Nets in Base 4

Best Known (112, 112+40, s)-Nets in Base 4

(112, 112+40, 531)-Net over F₄ — Constructive and digital

Digital (112, 152, 531)-net over F₄, using

t-expansion [i] based on digital (111, 152, 531)-net over F₄, using
- 4 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]

(112, 112+40, 1159)-Net over F₄ — Digital

Digital (112, 152, 1159)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 112+40, 104177)-Net in Base 4 — Upper bound on s

There is no (112, 152, 104178)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 32 596315 155329 689862 541714 200137 502529 788105 799185 549825 748195 309010 683145 317260 799002 407576 > 4¹⁵² [i]