MinT - Best Known (124−39, 124, s)-Nets in Base 5

Best Known (124−39, 124, s)-Nets in Base 5

(124−39, 124, 296)-Net over F₅ — Constructive and digital

Digital (85, 124, 296)-net over F₅, using

8 times m-reduction [i] based on digital (85, 132, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 66, 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]

(124−39, 124, 736)-Net over F₅ — Digital

Digital (85, 124, 736)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−39, 124, 66370)-Net in Base 5 — Upper bound on s

There is no (85, 124, 66371)-net in base 5, because

1 times m-reduction [i] would yield (85, 123, 66371)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 94 046631 154288 344800 828801 860471 478991 000894 768165 380101 306090 999312 901384 567891 612805 > 5¹²³ [i]