MinT - Best Known (118, 118+43, s)-Nets in Base 4

Best Known (118, 118+43, s)-Nets in Base 4

(118, 118+43, 531)-Net over F₄ — Constructive and digital

Digital (118, 161, 531)-net over F₄, using

t-expansion [i] based on digital (117, 161, 531)-net over F₄, using
- 4 times m-reduction [i] based on digital (117, 165, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 55, 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]

(118, 118+43, 1139)-Net over F₄ — Digital

Digital (118, 161, 1139)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(118, 118+43, 111796)-Net in Base 4 — Upper bound on s

There is no (118, 161, 111797)-net in base 4, because

1 times m-reduction [i] would yield (118, 160, 111797)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 136103 155254 822010 149809 107175 976325 924332 362844 458661 460124 168229 882941 647183 060361 744948 747852 > 4¹⁶⁰ [i]