MinT - Best Known (97−39, 97, s)-Nets in Base 5

Best Known (97−39, 97, s)-Nets in Base 5

(97−39, 97, 208)-Net over F₅ — Constructive and digital

Digital (58, 97, 208)-net over F₅, using

1 times m-reduction [i] based on digital (58, 98, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 49, 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]

(97−39, 97, 219)-Net over F₅ — Digital

Digital (58, 97, 219)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−39, 97, 6728)-Net in Base 5 — Upper bound on s

There is no (58, 97, 6729)-net in base 5, because

1 times m-reduction [i] would yield (58, 96, 6729)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 12 645526 075269 825812 633642 243691 015484 288366 153509 450434 193528 207325 > 5⁹⁶ [i]