MinT - Best Known (16, 16+45, s)-Nets in Base 8

Best Known (16, 16+45, s)-Nets in Base 8

(16, 16+45, 65)-Net over F₈ — Constructive and digital

Digital (16, 61, 65)-net over F₈, using

t-expansion [i] based on digital (14, 61, 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]

(16, 16+45, 362)-Net in Base 8 — Upper bound on s

There is no (16, 61, 363)-net in base 8, because

1 times m-reduction [i] would yield (16, 60, 363)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 614368 471772 093615 236412 489070 058048 173679 040398 079508 > 8⁶⁰ [i]