MinT - Best Known (88, 88+79, s)-Nets in Base 8

Best Known (88, 88+79, s)-Nets in Base 8

(88, 88+79, 208)-Net over F₈ — Constructive and digital

Digital (88, 167, 208)-net over F₈, using

3 times m-reduction [i] based on digital (88, 170, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 85, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(88, 88+79, 225)-Net in Base 8 — Constructive

(88, 167, 225)-net in base 8, using

t-expansion [i] based on (83, 167, 225)-net in base 8, using
- 5 times m-reduction [i] based on (83, 172, 225)-net in base 8, using
  - base change [i] based on digital (40, 129, 225)-net over F₁₆, using
    - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
        a function field by GarcÃa and Quoos [i]

(88, 88+79, 336)-Net over F₈ — Digital

Digital (88, 167, 336)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+79, 15330)-Net in Base 8 — Upper bound on s

There is no (88, 167, 15331)-net in base 8, because

1 times m-reduction [i] would yield (88, 166, 15331)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 819593 625085 351865 270981 410234 564545 233527 523884 256548 108530 783077 982066 469953 856024 443293 043881 617823 724842 123398 503045 434629 940878 543915 420906 065984 > 8¹⁶⁶ [i]