MinT - Best Known (30−15, 30, s)-Nets in Base 8

Best Known (30−15, 30, s)-Nets in Base 8

(30−15, 30, 130)-Net over F₈ — Constructive and digital

Digital (15, 30, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 15, 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]

(30−15, 30, 2657)-Net in Base 8 — Upper bound on s

There is no (15, 30, 2658)-net in base 8, because

1 times m-reduction [i] would yield (15, 29, 2658)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 154 778193 654067 622036 519920 > 8²⁹ [i]