MinT - Best Known (61, 61+34, s)-Nets in Base 25

Best Known (61, 61+34, s)-Nets in Base 25

(61, 61+34, 378)-Net over F₂₅ — Constructive and digital

Digital (61, 95, 378)-net over F₂₅, using

4 times m-reduction [i] based on digital (61, 99, 378)-net over F₂₅, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (10, 22, 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, 29, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)
  3. digital (10, 48, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(61, 61+34, 5818)-Net over F₂₅ — Digital

Digital (61, 95, 5818)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+34, large)-Net in Base 25 — Upper bound on s

There is no (61, 95, large)-net in base 25, because

32 times m-reduction [i] would yield (61, 63, large)-net in base 25, but
- mutually orthogonal hypercube bound [i]