MinT - Best Known (80, 80+49, s)-Nets in Base 8

Best Known (80, 80+49, s)-Nets in Base 8

(80, 80+49, 354)-Net over F₈ — Constructive and digital

Digital (80, 129, 354)-net over F₈, using

17 times m-reduction [i] based on digital (80, 146, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 73, 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]

(80, 80+49, 432)-Net in Base 8 — Constructive

(80, 129, 432)-net in base 8, using

1 times m-reduction [i] based on (80, 130, 432)-net in base 8, using
- trace code for nets [i] based on (15, 65, 216)-net in base 64, using
  - 5 times m-reduction [i] based on (15, 70, 216)-net in base 64, using
    - base change [i] based on digital (5, 60, 216)-net over F₁₂₈, using
      - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(80, 80+49, 730)-Net over F₈ — Digital

Digital (80, 129, 730)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+49, 91764)-Net in Base 8 — Upper bound on s

There is no (80, 129, 91765)-net in base 8, because

1 times m-reduction [i] would yield (80, 128, 91765)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 39 408724 027789 020696 105834 066836 620792 292360 110390 550665 950130 917850 490962 239336 476590 519694 060749 873663 668560 697244 > 8¹²⁸ [i]