MinT - Best Known (18−12, 18, s)-Nets in Base 7

Best Known (18−12, 18, s)-Nets in Base 7

(18−12, 18, 20)-Net over F₇ — Constructive and digital

Digital (6, 18, 20)-net over F₇, using

2 times m-reduction [i] based on digital (6, 20, 20)-net over F₇, using
- a shift-net [i]

(18−12, 18, 24)-Net over F₇ — Digital

Digital (6, 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]

(18−12, 18, 167)-Net in Base 7 — Upper bound on s

There is no (6, 18, 168)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1647 307625 738545 > 7¹⁸ [i]