MinT - Best Known (55, 96, s)-Nets in Base 25

Best Known (55, 96, s)-Nets in Base 25

(55, 96, 326)-Net over F₂₅ — Constructive and digital

Digital (55, 96, 326)-net over F₂₅, using

(u,Â u+v)-construction [i] based on
1. digital (10, 30, 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, 66, 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]

(55, 96, 1508)-Net over F₂₅ — Digital

Digital (55, 96, 1508)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 96, 1511148)-Net in Base 25 — Upper bound on s

There is no (55, 96, 1511149)-net in base 25, because

1 times m-reduction [i] would yield (55, 95, 1511149)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 6 372434 401933 417602 119501 722759 064042 497096 164971 372334 356996 920236 567275 983109 913745 099534 331951 482487 927907 663076 264180 513517 687521 > 25⁹⁵ [i]