MinT - Best Known (16−11, 16, s)-Nets in Base 7

Best Known (16−11, 16, s)-Nets in Base 7

(16−11, 16, 18)-Net over F₇ — Constructive and digital

Digital (5, 16, 18)-net over F₇, using

2 times m-reduction [i] based on digital (5, 18, 18)-net over F₇, using
- a shift-net [i]

(16−11, 16, 24)-Net over F₇ — Digital

Digital (5, 16, 24)-net over F₇, using

t-expansion [i] based on digital (4, 16, 24)-net over F₇, using
- net from sequence [i] based on digital (4, 23)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 4 and N(F) ≥ 24, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(16−11, 16, 146)-Net in Base 7 — Upper bound on s

There is no (5, 16, 147)-net in base 7, because

1 times m-reduction [i] would yield (5, 15, 147)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 4 890283 226011 > 7¹⁵ [i]