MinT - Best Known (138−60, 138, s)-Nets in Base 8

Best Known (138−60, 138, s)-Nets in Base 8

(138−60, 138, 354)-Net over F₈ — Constructive and digital

Digital (78, 138, 354)-net over F₈, using

4 times m-reduction [i] based on digital (78, 142, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 71, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(138−60, 138, 418)-Net over F₈ — Digital

Digital (78, 138, 418)-net over F₈, using

trace code for nets [i] based on digital (9, 69, 209)-net over F₆₄, using
- net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
    - a curve from the manYPoints database [i]

(138−60, 138, 24522)-Net in Base 8 — Upper bound on s

There is no (78, 138, 24523)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 42312 001803 210035 981198 785519 497466 139860 277273 616189 693507 446591 210771 834276 125339 143523 294368 605017 534285 215971 312611 839088 > 8¹³⁸ [i]