MinT - Best Known (47−22, 47, s)-Nets in Base 3

Best Known (47−22, 47, s)-Nets in Base 3

(47−22, 47, 32)-Net over F₃ — Constructive and digital

Digital (25, 47, 32)-net over F₃, using

t-expansion [i] based on digital (21, 47, 32)-net over F₃, using
- net from sequence [i] based on digital (21, 31)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
    - an explicitly constructive algebraic function field [i]

(47−22, 47, 40)-Net over F₃ — Digital

Digital (25, 47, 40)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(47−22, 47, 257)-Net in Base 3 — Upper bound on s

There is no (25, 47, 258)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 26641 149374 200339 993217 > 3⁴⁷ [i]