MinT - Best Known (69−49, 69, s)-Nets in Base 7

Best Known (69−49, 69, s)-Nets in Base 7

(69−49, 69, 28)-Net over F₇ — Constructive and digital

Digital (20, 69, 28)-net over F₇, using

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

(69−49, 69, 54)-Net over F₇ — Digital

Digital (20, 69, 54)-net over F₇, using

t-expansion [i] based on digital (19, 69, 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]

(69−49, 69, 389)-Net in Base 7 — Upper bound on s

There is no (20, 69, 390)-net in base 7, because

1 times m-reduction [i] would yield (20, 68, 390)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 2950 260804 844755 903140 392626 399397 577483 420570 882366 841649 > 7⁶⁸ [i]