MinT - Best Known (59, 102, s)-Nets in Base 25

Best Known (59, 102, s)-Nets in Base 25

(59, 102, 326)-Net over F₂₅ — Constructive and digital

Digital (59, 102, 326)-net over F₂₅, using

5 times m-reduction [i] based on digital (59, 107, 326)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 34, 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 (25, 73, 200)-net over F₂₅, using
    - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
        a function field by GarcÃa and Quoos [i]

(59, 102, 1729)-Net over F₂₅ — Digital

Digital (59, 102, 1729)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 102, 1912954)-Net in Base 25 — Upper bound on s

There is no (59, 102, 1912955)-net in base 25, because

1 times m-reduction [i] would yield (59, 101, 1912955)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1555 764449 294520 882996 730248 218273 830887 034961 325922 574121 565939 818503 060737 715503 926992 028171 604126 327906 653179 121216 052764 304461 203790 765865 > 25¹⁰¹ [i]