MinT - Best Known (212−58, 212, s)-Nets in Base 4

Best Known (212−58, 212, s)-Nets in Base 4

(212−58, 212, 531)-Net over F₄ — Constructive and digital

Digital (154, 212, 531)-net over F₄, using

t-expansion [i] based on digital (153, 212, 531)-net over F₄, using
- 7 times m-reduction [i] based on digital (153, 219, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 73, 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]

(212−58, 212, 1301)-Net over F₄ — Digital

Digital (154, 212, 1301)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−58, 212, 97985)-Net in Base 4 — Upper bound on s

There is no (154, 212, 97986)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 43 328707 742785 841703 258802 163800 586137 636806 763567 951142 838089 889757 742383 907881 586794 123843 058024 584752 749760 748093 031112 918736 > 4²¹² [i]