MinT - Best Known (180−49, 180, s)-Nets in Base 4

Best Known (180−49, 180, s)-Nets in Base 4

(180−49, 180, 531)-Net over F₄ — Constructive and digital

Digital (131, 180, 531)-net over F₄, using

6 times m-reduction [i] based on digital (131, 186, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 62, 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]

(180−49, 180, 1155)-Net over F₄ — Digital

Digital (131, 180, 1155)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−49, 180, 101046)-Net in Base 4 — Upper bound on s

There is no (131, 180, 101047)-net in base 4, because

1 times m-reduction [i] would yield (131, 179, 101047)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 587188 739887 067277 498637 077710 008825 869879 443268 649744 809737 202115 032762 562611 326786 210540 884326 455479 537924 > 4¹⁷⁹ [i]