MinT - Best Known (45, 84, s)-Nets in Base 7

Best Known (45, 84, s)-Nets in Base 7

(45, 84, 106)-Net over F₇ — Constructive and digital

Digital (45, 84, 106)-net over F₇, using

trace code for nets [i] based on digital (3, 42, 53)-net over F₄₉, using
- net from sequence [i] based on digital (3, 52)-sequence over F₄₉, using
  - Niederreiter sequence [i]

(45, 84, 184)-Net over F₇ — Digital

Digital (45, 84, 184)-net over F₇, using

trace code for nets [i] based on digital (3, 42, 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]

(45, 84, 6486)-Net in Base 7 — Upper bound on s

There is no (45, 84, 6487)-net in base 7, because

1 times m-reduction [i] would yield (45, 83, 6487)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 13933 670278 972883 834608 287754 571554 954046 384510 141571 892954 756681 332559 > 7⁸³ [i]