MinT - Best Known (72, 72+55, s)-Nets in Base 8

Best Known (72, 72+55, s)-Nets in Base 8

(72, 72+55, 354)-Net over F₈ — Constructive and digital

Digital (72, 127, 354)-net over F₈, using

3 times m-reduction [i] based on digital (72, 130, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 65, 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]

(72, 72+55, 387)-Net over F₈ — Digital

Digital (72, 127, 387)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+55, 25553)-Net in Base 8 — Upper bound on s

There is no (72, 127, 25554)-net in base 8, because

1 times m-reduction [i] would yield (72, 126, 25554)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 616290 451324 472306 773452 161416 169955 543939 817485 674713 751258 595164 544547 386713 395451 460890 307155 775612 021357 209184 > 8¹²⁶ [i]