MinT - Best Known (105, 105+41, s)-Nets in Base 3

Best Known (105, 105+41, s)-Nets in Base 3

(105, 105+41, 246)-Net over F₃ — Constructive and digital

Digital (105, 146, 246)-net over F₃, using

1 times m-reduction [i] based on digital (105, 147, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 49, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(105, 105+41, 426)-Net over F₃ — Digital

Digital (105, 146, 426)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+41, 11931)-Net in Base 3 — Upper bound on s

There is no (105, 146, 11932)-net in base 3, because

1 times m-reduction [i] would yield (105, 145, 11932)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1523 750794 598098 967924 615172 320199 776529 399362 445877 032139 948431 810177 > 3¹⁴⁵ [i]