MinT - Best Known (87−41, 87, s)-Nets in Base 4

Best Known (87−41, 87, s)-Nets in Base 4

(87−41, 87, 66)-Net over F₄ — Constructive and digital

Digital (46, 87, 66)-net over F₄, using

1 times m-reduction [i] based on digital (46, 88, 66)-net over F₄, using
- trace code for nets [i] based on digital (2, 44, 33)-net over F₁₆, using
  - net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
      - a function field by SÃ©mirat [i]

(87−41, 87, 87)-Net over F₄ — Digital

Digital (46, 87, 87)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−41, 87, 1058)-Net in Base 4 — Upper bound on s

There is no (46, 87, 1059)-net in base 4, because

1 times m-reduction [i] would yield (46, 86, 1059)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6096 247789 218894 920889 987432 053835 595763 040145 121944 > 4⁸⁶ [i]