MinT - Best Known (93−26, 93, s)-Nets in Base 5

Best Known (93−26, 93, s)-Nets in Base 5

(93−26, 93, 296)-Net over F₅ — Constructive and digital

Digital (67, 93, 296)-net over F₅, using

3 times m-reduction [i] based on digital (67, 96, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 48, 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]

(93−26, 93, 1026)-Net over F₅ — Digital

Digital (67, 93, 1026)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(93−26, 93, 141788)-Net in Base 5 — Upper bound on s

There is no (67, 93, 141789)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 100976 633071 026711 824388 986418 096462 965135 572028 134817 102030 646789 > 5⁹³ [i]