MinT - Best Known (105−32, 105, s)-Nets in Base 5

Best Known (105−32, 105, s)-Nets in Base 5

(105−32, 105, 296)-Net over F₅ — Constructive and digital

Digital (73, 105, 296)-net over F₅, using

3 times m-reduction [i] based on digital (73, 108, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 54, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(105−32, 105, 739)-Net over F₅ — Digital

Digital (73, 105, 739)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−32, 105, 65673)-Net in Base 5 — Upper bound on s

There is no (73, 105, 65674)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 24 652010 948418 566212 810502 495115 444470 262830 565885 605564 056479 993334 735617 > 5¹⁰⁵ [i]