MinT - Best Known (139−109, 139, s)-Nets in Base 8

Best Known (139−109, 139, s)-Nets in Base 8

(139−109, 139, 65)-Net over F₈ — Constructive and digital

Digital (30, 139, 65)-net over F₈, using

t-expansion [i] based on digital (14, 139, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(139−109, 139, 97)-Net over F₈ — Digital

Digital (30, 139, 97)-net over F₈, using

t-expansion [i] based on digital (28, 139, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(139−109, 139, 574)-Net in Base 8 — Upper bound on s

There is no (30, 139, 575)-net in base 8, because

1 times m-reduction [i] would yield (30, 138, 575)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 42423 508558 669032 426779 408724 884386 384637 768879 963065 230304 499488 697453 771723 795646 021487 596273 073903 883333 029438 875388 328497 > 8¹³⁸ [i]