MinT - Best Known (60, 60+35, s)-Nets in Base 8

Best Known (60, 60+35, s)-Nets in Base 8

(60, 60+35, 354)-Net over F₈ — Constructive and digital

Digital (60, 95, 354)-net over F₈, using

11 times m-reduction [i] based on digital (60, 106, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 53, 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]

(60, 60+35, 514)-Net in Base 8 — Constructive

(60, 95, 514)-net in base 8, using

1 times m-reduction [i] based on (60, 96, 514)-net in base 8, using
- base change [i] based on digital (36, 72, 514)-net over F₁₆, using
  - trace code for nets [i] based on digital (0, 36, 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]

(60, 60+35, 662)-Net over F₈ — Digital

Digital (60, 95, 662)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+35, 101008)-Net in Base 8 — Upper bound on s

There is no (60, 95, 101009)-net in base 8, because

1 times m-reduction [i] would yield (60, 94, 101009)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 7 771083 377042 045706 995087 833012 101582 544312 942445 552752 336048 243090 356411 594376 723912 > 8⁹⁴ [i]