MinT - Best Known (142−40, 142, s)-Nets in Base 4

Best Known (142−40, 142, s)-Nets in Base 4

(142−40, 142, 531)-Net over F₄ — Constructive and digital

Digital (102, 142, 531)-net over F₄, using

4¹ times duplication [i] based on digital (101, 141, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 47, 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]

(142−40, 142, 818)-Net over F₄ — Digital

Digital (102, 142, 818)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−40, 142, 52080)-Net in Base 4 — Upper bound on s

There is no (102, 142, 52081)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31 087245 724925 954216 370039 908708 261723 271349 768444 905994 799589 795209 971852 095976 635544 > 4¹⁴² [i]