MinT - Best Known (11, 11+12, s)-Nets in Base 5

Best Known (11, 11+12, s)-Nets in Base 5

(11, 11+12, 32)-Net over F₅ — Constructive and digital

Digital (11, 23, 32)-net over F₅, using

net from sequence [i] based on digital (11, 31)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 11 and N(F) ≥ 32, using
  - an explicitly constructive algebraic function field [i]

(11, 11+12, 35)-Net over F₅ — Digital

Digital (11, 23, 35)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(11, 11+12, 353)-Net in Base 5 — Upper bound on s

There is no (11, 23, 354)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 11972 950224 835585 > 5²³ [i]