MinT - Best Known (90−42, 90, s)-Nets in Base 7

Best Known (90−42, 90, s)-Nets in Base 7

(90−42, 90, 106)-Net over F₇ — Constructive and digital

Digital (48, 90, 106)-net over F₇, using

trace code for nets [i] based on digital (3, 45, 53)-net over F₄₉, using
- net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(90−42, 90, 184)-Net over F₇ — Digital

Digital (48, 90, 184)-net over F₇, using

trace code for nets [i] based on digital (3, 45, 92)-net over F₄₉, using
- net from sequence [i] based on digital (3, 91)-sequence over F₄₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 3 and N(F) ≥ 92, using
    - a curve from the manYPoints database [i]

(90−42, 90, 6042)-Net in Base 7 — Upper bound on s

There is no (48, 90, 6043)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 11467 633440 829581 237487 759292 542841 211454 791060 249538 737641 577120 958145 472043 > 7⁹⁰ [i]