MinT - Best Known (144−39, 144, s)-Nets in Base 4

Best Known (144−39, 144, s)-Nets in Base 4

(144−39, 144, 531)-Net over F₄ — Constructive and digital

Digital (105, 144, 531)-net over F₄, using

3 times m-reduction [i] based on digital (105, 147, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 49, 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]

(144−39, 144, 976)-Net over F₄ — Digital

Digital (105, 144, 976)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−39, 144, 89807)-Net in Base 4 — Upper bound on s

There is no (105, 144, 89808)-net in base 4, because

1 times m-reduction [i] would yield (105, 143, 89808)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 124 337837 735756 768433 553542 767740 824281 758137 972951 106435 596149 643417 526366 095047 427628 > 4¹⁴³ [i]