MinT - Best Known (111−34, 111, s)-Nets in Base 3

Best Known (111−34, 111, s)-Nets in Base 3

(111−34, 111, 156)-Net over F₃ — Constructive and digital

Digital (77, 111, 156)-net over F₃, using

trace code for nets [i] based on digital (3, 37, 52)-net over F₂₇, using
- net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
    - a function field by SÃ©mirat [i]

(111−34, 111, 255)-Net over F₃ — Digital

Digital (77, 111, 255)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(111−34, 111, 4663)-Net in Base 3 — Upper bound on s

There is no (77, 111, 4664)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 91489 511181 459716 124478 790715 125403 229815 258291 660657 > 3¹¹¹ [i]