MinT - Best Known (17, 17+25, s)-Nets in Base 7

Best Known (17, 17+25, s)-Nets in Base 7

(17, 17+25, 25)-Net over F₇ — Constructive and digital

Digital (17, 42, 25)-net over F₇, using

net from sequence [i] based on digital (17, 24)-sequence over F₇, using
- Niederreiter sequence [i]

(17, 17+25, 48)-Net over F₇ — Digital

Digital (17, 42, 48)-net over F₇, using

t-expansion [i] based on digital (13, 42, 48)-net over F₇, using
- net from sequence [i] based on digital (13, 47)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 13 and N(F) ≥ 48, using
    - an algebraic function field by Teo [i]

(17, 17+25, 672)-Net in Base 7 — Upper bound on s

There is no (17, 42, 673)-net in base 7, because

1 times m-reduction [i] would yield (17, 41, 673)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 44792 472380 788656 545368 673832 851233 > 7⁴¹ [i]