MinT - Best Known (124−34, 124, s)-Nets in Base 4

Best Known (124−34, 124, s)-Nets in Base 4

(124−34, 124, 531)-Net over F₄ — Constructive and digital

Digital (90, 124, 531)-net over F₄, using

4¹ times duplication [i] based on digital (89, 123, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 41, 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]

(124−34, 124, 819)-Net over F₄ — Digital

Digital (90, 124, 819)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−34, 124, 58914)-Net in Base 4 — Upper bound on s

There is no (90, 124, 58915)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 452 423455 037482 343511 250998 921239 381728 813053 816679 645748 947950 728553 211900 > 4¹²⁴ [i]