MinT - Best Known (30, 30+30, s)-Nets in Base 8

Best Known (30, 30+30, s)-Nets in Base 8

(30, 30+30, 130)-Net over F₈ — Constructive and digital

Digital (30, 60, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 30, 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]

(30, 30+30, 3749)-Net in Base 8 — Upper bound on s

There is no (30, 60, 3750)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 535646 486382 219521 170326 876991 490200 401507 873640 875376 > 8⁶⁰ [i]