MinT - Best Known (17, 17+57, s)-Nets in Base 8

Best Known (17, 17+57, s)-Nets in Base 8

(17, 17+57, 65)-Net over F₈ — Constructive and digital

Digital (17, 74, 65)-net over F₈, using

t-expansion [i] based on digital (14, 74, 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]

(17, 17+57, 347)-Net in Base 8 — Upper bound on s

There is no (17, 74, 348)-net in base 8, because

1 times m-reduction [i] would yield (17, 73, 348)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 853138 080950 452560 614368 299193 853623 829075 693990 951294 362358 422544 > 8⁷³ [i]