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

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

(26, 26+26, 52)-Net over F₅ — Constructive and digital

Digital (26, 52, 52)-net over F₅, using

trace code for nets [i] based on digital (0, 26, 26)-net over F₂₅, using
- net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
    - the rational function field F₂₅(x) [i]
  - Niederreiter sequence [i]

(26, 26+26, 64)-Net over F₅ — Digital

Digital (26, 52, 64)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(26, 26+26, 876)-Net in Base 5 — Upper bound on s

There is no (26, 52, 877)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 241332 737993 982833 483668 285937 837125 > 5⁵² [i]