MinT - Best Known (106, 106+77, s)-Nets in Base 3

Best Known (106, 106+77, s)-Nets in Base 3

(106, 106+77, 128)-Net over F₃ — Constructive and digital

Digital (106, 183, 128)-net over F₃, using

3 times m-reduction [i] based on digital (106, 186, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 93, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(106, 106+77, 150)-Net over F₃ — Digital

Digital (106, 183, 150)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 106+77, 1411)-Net in Base 3 — Upper bound on s

There is no (106, 183, 1412)-net in base 3, because

1 times m-reduction [i] would yield (106, 182, 1412)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 695 605576 747184 835821 173528 446766 541551 139276 069231 381625 049349 412186 936875 993295 081945 > 3¹⁸² [i]