MinT - Best Known (87−29, 87, s)-Nets in Base 4

Best Known (87−29, 87, s)-Nets in Base 4

(87−29, 87, 195)-Net over F₄ — Constructive and digital

Digital (58, 87, 195)-net over F₄, using

trace code for nets [i] based on digital (0, 29, 65)-net over F₆₄, using
- net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
    - the rational function field F₆₄(x) [i]
  - Niederreiter sequence [i]

(87−29, 87, 283)-Net over F₄ — Digital

Digital (58, 87, 283)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(87−29, 87, 10051)-Net in Base 4 — Upper bound on s

There is no (58, 87, 10052)-net in base 4, because

1 times m-reduction [i] would yield (58, 86, 10052)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 5991 997414 189246 489992 670968 700648 925889 440493 398224 > 4⁸⁶ [i]