MinT - Best Known (56, 97, s)-Nets in Base 25

Best Known (56, 97, s)-Nets in Base 25

(56, 97, 326)-Net over F₂₅ — Constructive and digital

Digital (56, 97, 326)-net over F₂₅, using

1 times m-reduction [i] based on digital (56, 98, 326)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 31, 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, 67, 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]

(56, 97, 1633)-Net over F₂₅ — Digital

Digital (56, 97, 1633)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 97, 1775025)-Net in Base 25 — Upper bound on s

There is no (56, 97, 1775026)-net in base 25, because

1 times m-reduction [i] would yield (56, 96, 1775026)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 159 310778 161664 307515 163292 278766 917264 382480 484607 773668 260196 262373 685131 677688 484913 210981 364627 424279 473185 111277 728560 527218 877505 > 25⁹⁶ [i]