MinT - Best Known (59, 59+59, s)-Nets in Base 8

Best Known (59, 59+59, s)-Nets in Base 8

(59, 59+59, 130)-Net over F₈ — Constructive and digital

Digital (59, 118, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 59, 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]

(59, 59+59, 199)-Net over F₈ — Digital

Digital (59, 118, 199)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+59, 7318)-Net in Base 8 — Upper bound on s

There is no (59, 118, 7319)-net in base 8, because

1 times m-reduction [i] would yield (59, 117, 7319)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4587 361282 615112 216335 978346 304349 128059 269132 465248 067429 484874 054895 326394 238526 423631 627359 321728 572896 > 8¹¹⁷ [i]