MinT - Best Known (59−39, 59, s)-Nets in Base 7

Best Known (59−39, 59, s)-Nets in Base 7

(59−39, 59, 28)-Net over F₇ — Constructive and digital

Digital (20, 59, 28)-net over F₇, using

net from sequence [i] based on digital (20, 27)-sequence over F₇, using
- Niederreiter sequence [i]

(59−39, 59, 54)-Net over F₇ — Digital

Digital (20, 59, 54)-net over F₇, using

t-expansion [i] based on digital (19, 59, 54)-net over F₇, using
- net from sequence [i] based on digital (19, 53)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 19 and N(F) ≥ 54, using
    - an algebraic function field by Teo [i]

(59−39, 59, 490)-Net in Base 7 — Upper bound on s

There is no (20, 59, 491)-net in base 7, because

1 times m-reduction [i] would yield (20, 58, 491)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 10 733650 603542 417573 101518 427994 122859 608554 235023 > 7⁵⁸ [i]