MinT - Best Known (80, 80+48, s)-Nets in Base 8

Best Known (80, 80+48, s)-Nets in Base 8

(80, 80+48, 354)-Net over F₈ — Constructive and digital

Digital (80, 128, 354)-net over F₈, using

18 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+48, 514)-Net in Base 8 — Constructive

(80, 128, 514)-net in base 8, using

base change [i] based on digital (48, 96, 514)-net over F₁₆, using
- trace code for nets [i] based on digital (0, 48, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(80, 80+48, 775)-Net over F₈ — Digital

Digital (80, 128, 775)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+48, 91764)-Net in Base 8 — Upper bound on s

There is no (80, 128, 91765)-net in base 8, because

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]