MinT - Best Known (63, 63+39, s)-Nets in Base 25

Best Known (63, 63+39, s)-Nets in Base 25

(63, 63+39, 378)-Net over F₂₅ — Constructive and digital

Digital (63, 102, 378)-net over F₂₅, using

2 times m-reduction [i] based on digital (63, 104, 378)-net over F₂₅, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (10, 23, 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, 30, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)
  3. digital (10, 51, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(63, 63+39, 3559)-Net over F₂₅ — Digital

Digital (63, 102, 3559)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+39, large)-Net in Base 25 — Upper bound on s

There is no (63, 102, large)-net in base 25, because

37 times m-reduction [i] would yield (63, 65, large)-net in base 25, but
- mutually orthogonal hypercube bound [i]