MinT - Best Known (97−28, 97, s)-Nets in Base 5

Best Known (97−28, 97, s)-Nets in Base 5

(97−28, 97, 296)-Net over F₅ — Constructive and digital

Digital (69, 97, 296)-net over F₅, using

3 times m-reduction [i] based on digital (69, 100, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 50, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(97−28, 97, 899)-Net over F₅ — Digital

Digital (69, 97, 899)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−28, 97, 105249)-Net in Base 5 — Upper bound on s

There is no (69, 97, 105250)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 63 112971 178167 161493 858941 121623 536704 384848 337182 675918 812081 692801 > 5⁹⁷ [i]