MinT - Best Known (87−36, 87, s)-Nets in Base 4

Best Known (87−36, 87, s)-Nets in Base 4

(87−36, 87, 130)-Net over F₄ — Constructive and digital

Digital (51, 87, 130)-net over F₄, using

3 times m-reduction [i] based on digital (51, 90, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 45, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(87−36, 87, 133)-Net over F₄ — Digital

Digital (51, 87, 133)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−36, 87, 2031)-Net in Base 4 — Upper bound on s

There is no (51, 87, 2032)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 23982 891678 677969 164977 650130 048170 142468 835308 305494 > 4⁸⁷ [i]