MinT - Best Known (139−38, 139, s)-Nets in Base 4

Best Known (139−38, 139, s)-Nets in Base 4

(139−38, 139, 531)-Net over F₄ — Constructive and digital

Digital (101, 139, 531)-net over F₄, using

2 times m-reduction [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]

(139−38, 139, 911)-Net over F₄ — Digital

Digital (101, 139, 911)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−38, 139, 67071)-Net in Base 4 — Upper bound on s

There is no (101, 139, 67072)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 485712 309071 158520 973319 019006 880287 495976 497570 206103 154128 462391 316337 764655 905249 > 4¹³⁹ [i]