MinT - Best Known (87−39, 87, s)-Nets in Base 4

Best Known (87−39, 87, s)-Nets in Base 4

(87−39, 87, 90)-Net over F₄ — Constructive and digital

Digital (48, 87, 90)-net over F₄, using

1 times m-reduction [i] based on digital (48, 88, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 44, 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]

(87−39, 87, 102)-Net over F₄ — Digital

Digital (48, 87, 102)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−39, 87, 1388)-Net in Base 4 — Upper bound on s

There is no (48, 87, 1389)-net in base 4, because

1 times m-reduction [i] would yield (48, 86, 1389)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6050 126353 811590 047305 322611 867637 725847 453655 761160 > 4⁸⁶ [i]