MinT - Best Known (108, 108+40, s)-Nets in Base 3

Best Known (108, 108+40, s)-Nets in Base 3

(108, 108+40, 264)-Net over F₃ — Constructive and digital

Digital (108, 148, 264)-net over F₃, using

3¹ times duplication [i] based on digital (107, 147, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 49, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(108, 108+40, 495)-Net over F₃ — Digital

Digital (108, 148, 495)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+40, 14072)-Net in Base 3 — Upper bound on s

There is no (108, 148, 14073)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 41136 677509 033504 923028 394716 894849 569584 129301 300302 727349 105361 416401 > 3¹⁴⁸ [i]