MinT - Best Known (146, 146+62, s)-Nets in Base 4

Best Known (146, 146+62, s)-Nets in Base 4

(146, 146+62, 531)-Net over F₄ — Constructive and digital

Digital (146, 208, 531)-net over F₄, using

4¹ times duplication [i] based on digital (145, 207, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 69, 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]

(146, 146+62, 881)-Net over F₄ — Digital

Digital (146, 208, 881)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(146, 146+62, 45320)-Net in Base 4 — Upper bound on s

There is no (146, 208, 45321)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 169255 571263 793804 797847 372192 084510 484047 384254 552517 229769 875857 655932 116722 438301 422509 823184 271591 617697 461545 065407 317760 > 4²⁰⁸ [i]