MinT - Best Known (67−47, 67, s)-Nets in Base 7

Best Known (67−47, 67, s)-Nets in Base 7

(67−47, 67, 28)-Net over F₇ — Constructive and digital

Digital (20, 67, 28)-net over F₇, using

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

(67−47, 67, 54)-Net over F₇ — Digital

Digital (20, 67, 54)-net over F₇, using

t-expansion [i] based on digital (19, 67, 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]

(67−47, 67, 403)-Net in Base 7 — Upper bound on s

There is no (20, 67, 404)-net in base 7, because

1 times m-reduction [i] would yield (20, 66, 404)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 61 367306 612326 505708 345925 991743 265941 888740 640478 876513 > 7⁶⁶ [i]