MinT - Best Known (45, 45+44, s)-Nets in Base 7

Best Known (45, 45+44, s)-Nets in Base 7

(45, 45+44, 100)-Net over F₇ — Constructive and digital

Digital (45, 89, 100)-net over F₇, using

1 times m-reduction [i] based on digital (45, 90, 100)-net over F₇, using
- trace code for nets [i] based on digital (0, 45, 50)-net over F₄₉, using
  - net from sequence [i] based on digital (0, 49)-sequence over F₄₉, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using
      - the rational function field F₄₉(x) [i]
    - Niederreiter sequence [i]

(45, 45+44, 144)-Net over F₇ — Digital

Digital (45, 89, 144)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(45, 45+44, 3944)-Net in Base 7 — Upper bound on s

There is no (45, 89, 3945)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 1643 631999 939480 506338 920319 911271 411165 061054 230588 875283 336787 744991 194977 > 7⁸⁹ [i]