MinT - Best Known (32, 64, s)-Nets in Base 8

Best Known (32, 64, s)-Nets in Base 8

(32, 64, 130)-Net over F₈ — Constructive and digital

Digital (32, 64, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 32, 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]

(32, 64, 3969)-Net in Base 8 — Upper bound on s

There is no (32, 64, 3970)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6290 581925 534046 538474 888370 770120 859054 078869 252748 367880 > 8⁶⁴ [i]