MinT - Best Known (102−41, 102, s)-Nets in Base 25

Best Known (102−41, 102, s)-Nets in Base 25

(102−41, 102, 334)-Net over F₂₅ — Constructive and digital

Digital (61, 102, 334)-net over F₂₅, using

generalized (u,Â u+v)-construction [i] based on
1. digital (9, 22, 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, 29, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-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, 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]

(102−41, 102, 2432)-Net over F₂₅ — Digital

Digital (61, 102, 2432)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(102−41, 102, 3969089)-Net in Base 25 — Upper bound on s

There is no (61, 102, 3969090)-net in base 25, because

1 times m-reduction [i] would yield (61, 101, 3969090)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1555 757006 195887 209909 643878 707127 711290 931957 455742 505754 660418 425082 336084 594694 585091 563135 615155 690250 365005 789420 429490 680191 925654 167105 > 25¹⁰¹ [i]