MinT - Best Known (58, 58+36, s)-Nets in Base 25

Best Known (58, 58+36, s)-Nets in Base 25

(58, 58+36, 334)-Net over F₂₅ — Constructive and digital

Digital (58, 94, 334)-net over F₂₅, using

1 times m-reduction [i] based on digital (58, 95, 334)-net over F₂₅, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (9, 21, 104)-net over F₂₅, using
    - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
        a function field by GarcÃa and Quoos [i]
  2. digital (9, 27, 104)-net over F₂₅, using
    - net from sequence [i] based on digital (9, 103)-sequence over F₂₅ (see above)
  3. digital (10, 47, 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]

(58, 58+36, 3310)-Net over F₂₅ — Digital

Digital (58, 94, 3310)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+36, 6284511)-Net in Base 25 — Upper bound on s

There is no (58, 94, 6284512)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 254894 763587 268893 625438 047879 670399 884532 669159 430885 338946 718786 259758 667764 335588 328013 915434 419463 511536 937965 167185 089253 594625 > 25⁹⁴ [i]