MinT - Best Known (145−72, 145, s)-Nets in Base 8

Best Known (145−72, 145, s)-Nets in Base 8

(145−72, 145, 130)-Net over F₈ — Constructive and digital

Digital (73, 145, 130)-net over F₈, using

1 times m-reduction [i] based on digital (73, 146, 130)-net over F₈, using
- trace code for nets [i] based on digital (0, 73, 65)-net over F₆₄, using
  - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
      - the rational function field F₆₄(x) [i]
    - Niederreiter sequence [i]

(145−72, 145, 244)-Net over F₈ — Digital

Digital (73, 145, 244)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−72, 145, 8830)-Net in Base 8 — Upper bound on s

There is no (73, 145, 8831)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 88992 830202 673410 193894 336273 320895 207099 261316 289965 359167 376893 586533 966420 041792 189524 554651 699045 231113 701116 762127 879649 982937 > 8¹⁴⁵ [i]