MinT - Best Known (104, 104+38, s)-Nets in Base 3

Best Known (104, 104+38, s)-Nets in Base 3

(104, 104+38, 264)-Net over F₃ — Constructive and digital

Digital (104, 142, 264)-net over F₃, using

3¹ times duplication [i] based on digital (103, 141, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 47, 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]

(104, 104+38, 498)-Net over F₃ — Digital

Digital (104, 142, 498)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(104, 104+38, 14570)-Net in Base 3 — Upper bound on s

There is no (104, 142, 14571)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 56 394598 040306 088074 720113 060182 418583 982805 717365 211588 817686 249131 > 3¹⁴² [i]