MinT - Best Known (88−29, 88, s)-Nets in Base 4

Best Known (88−29, 88, s)-Nets in Base 4

(88−29, 88, 195)-Net over F₄ — Constructive and digital

Digital (59, 88, 195)-net over F₄, using

4¹ times duplication [i] based on 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]

(88−29, 88, 299)-Net over F₄ — Digital

Digital (59, 88, 299)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−29, 88, 11098)-Net in Base 4 — Upper bound on s

There is no (59, 88, 11099)-net in base 4, because

1 times m-reduction [i] would yield (59, 87, 11099)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 23953 824219 651558 273771 124212 248603 085185 668317 180724 > 4⁸⁷ [i]