MinT - Best Known (95−44, 95, s)-Nets in Base 8

Best Known (95−44, 95, s)-Nets in Base 8

(95−44, 95, 208)-Net over F₈ — Constructive and digital

Digital (51, 95, 208)-net over F₈, using

1 times m-reduction [i] based on digital (51, 96, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 48, 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]

(95−44, 95, 229)-Net over F₈ — Digital

Digital (51, 95, 229)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(95−44, 95, 10253)-Net in Base 8 — Upper bound on s

There is no (51, 95, 10254)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 62 193018 847796 423470 656523 057746 054588 301265 304507 453454 174907 056112 465498 958609 823232 > 8⁹⁵ [i]