MinT - Best Known (39−27, 39, s)-Nets in Base 7

Best Known (39−27, 39, s)-Nets in Base 7

(39−27, 39, 20)-Net over F₇ — Constructive and digital

Digital (12, 39, 20)-net over F₇, using

net from sequence [i] based on digital (12, 19)-sequence over F₇, using
- Niederreiter sequence [i]

(39−27, 39, 38)-Net over F₇ — Digital

Digital (12, 39, 38)-net over F₇, using

t-expansion [i] based on digital (9, 39, 38)-net over F₇, using
- net from sequence [i] based on digital (9, 37)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 9 and N(F) ≥ 38, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(39−27, 39, 270)-Net in Base 7 — Upper bound on s

There is no (12, 39, 271)-net in base 7, because

1 times m-reduction [i] would yield (12, 38, 271)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 130 714727 125390 670967 274337 023123 > 7³⁸ [i]