MinT - Best Known (244−74, 244, s)-Nets in Base 4

Best Known (244−74, 244, s)-Nets in Base 4

(244−74, 244, 531)-Net over F₄ — Constructive and digital

Digital (170, 244, 531)-net over F₄, using

4¹ times duplication [i] based on digital (169, 243, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 81, 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]

(244−74, 244, 941)-Net over F₄ — Digital

Digital (170, 244, 941)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−74, 244, 45587)-Net in Base 4 — Upper bound on s

There is no (170, 244, 45588)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 799 659598 975145 408439 661477 508858 373724 933865 074935 024060 252779 561020 124565 812489 966978 790180 796138 084919 177241 709175 029084 054962 025632 442444 199872 > 4²⁴⁴ [i]