MinT - Best Known (111, 111+46, s)-Nets in Base 3

Best Known (111, 111+46, s)-Nets in Base 3

(111, 111+46, 228)-Net over F₃ — Constructive and digital

Digital (111, 157, 228)-net over F₃, using

3¹ times duplication [i] based on digital (110, 156, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 52, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(111, 111+46, 390)-Net over F₃ — Digital

Digital (111, 157, 390)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+46, 8494)-Net in Base 3 — Upper bound on s

There is no (111, 157, 8495)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 809 740070 535277 560700 733365 333158 366566 751774 322809 101010 049207 637810 993043 > 3¹⁵⁷ [i]