MinT - Best Known (69, 105, s)-Nets in Base 5

Best Known (69, 105, s)-Nets in Base 5

(69, 105, 252)-Net over F₅ — Constructive and digital

Digital (69, 105, 252)-net over F₅, using

13 times m-reduction [i] based on digital (69, 118, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 59, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(69, 105, 444)-Net over F₅ — Digital

Digital (69, 105, 444)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 105, 22549)-Net in Base 5 — Upper bound on s

There is no (69, 105, 22550)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 24 653640 807505 498914 924935 310595 093760 857532 630757 284622 028190 466042 618241 > 5¹⁰⁵ [i]