MinT - Best Known (22−12, 22, s)-Nets in Base 5

Best Known (22−12, 22, s)-Nets in Base 5

(22−12, 22, 26)-Net over F₅ — Constructive and digital

Digital (10, 22, 26)-net over F₅, using

t-expansion [i] based on digital (9, 22, 26)-net over F₅, using
- net from sequence [i] based on digital (9, 25)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 9 and N(F) ≥ 26, using
    - an explicitly constructive algebraic function field [i]

(22−12, 22, 29)-Net over F₅ — Digital

Digital (10, 22, 29)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(22−12, 22, 269)-Net in Base 5 — Upper bound on s

There is no (10, 22, 270)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2406 127667 230657 > 5²² [i]