MinT - Best Known (258−71, 258, s)-Nets in Base 4

Best Known (258−71, 258, s)-Nets in Base 4

(258−71, 258, 531)-Net over F₄ — Constructive and digital

Digital (187, 258, 531)-net over F₄, using

t-expansion [i] based on digital (179, 258, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 86, 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]

(258−71, 258, 1494)-Net over F₄ — Digital

Digital (187, 258, 1494)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(258−71, 258, 122146)-Net in Base 4 — Upper bound on s

There is no (187, 258, 122147)-net in base 4, because

1 times m-reduction [i] would yield (187, 257, 122147)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53638 430025 584100 578953 844432 357999 451864 409719 384375 149583 224184 896744 631062 159317 541915 431106 271031 220232 200746 016782 067675 399993 226611 929200 961323 201004 > 4²⁵⁷ [i]