MinT - Best Known (65, 65+39, s)-Nets in Base 25

Best Known (65, 65+39, s)-Nets in Base 25

(65, 65+39, 378)-Net over F₂₅ — Constructive and digital

Digital (65, 104, 378)-net over F₂₅, using

4 times m-reduction [i] based on digital (65, 108, 378)-net over F₂₅, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (10, 24, 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]
  2. digital (10, 31, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)
  3. digital (10, 53, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(65, 65+39, 4212)-Net over F₂₅ — Digital

Digital (65, 104, 4212)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+39, large)-Net in Base 25 — Upper bound on s

There is no (65, 104, large)-net in base 25, because

37 times m-reduction [i] would yield (65, 67, large)-net in base 25, but
- mutually orthogonal hypercube bound [i]