MinT - Best Known (5, 5+13, s)-Nets in Base 7

Best Known (5, 5+13, s)-Nets in Base 7

(5, 5+13, 18)-Net over F₇ — Constructive and digital

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

a shift-net [i]

(5, 5+13, 24)-Net over F₇ — Digital

Digital (5, 18, 24)-net over F₇, using

t-expansion [i] based on digital (4, 18, 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]

(5, 5+13, 120)-Net in Base 7 — Upper bound on s

There is no (5, 18, 121)-net in base 7, because

1 times m-reduction [i] would yield (5, 17, 121)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 240 914088 493057 > 7¹⁷ [i]