MinT - Best Known (49, 89, s)-Nets in Base 4

Best Known (49, 89, s)-Nets in Base 4

(49, 89, 90)-Net over F₄ — Constructive and digital

Digital (49, 89, 90)-net over F₄, using

1 times m-reduction [i] based on digital (49, 90, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 45, 45)-net over F₁₆, using
  - net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]

(49, 89, 102)-Net over F₄ — Digital

Digital (49, 89, 102)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 89, 1306)-Net in Base 4 — Upper bound on s

There is no (49, 89, 1307)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 387340 736092 894393 081321 515249 235739 902550 364913 386934 > 4⁸⁹ [i]