MinT - Best Known (158, 158+69, s)-Nets in Base 3

Best Known (158, 158+69, s)-Nets in Base 3

(158, 158+69, 228)-Net over F₃ — Constructive and digital

Digital (158, 227, 228)-net over F₃, using

1 times m-reduction [i] based on digital (158, 228, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 76, 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]

(158, 158+69, 475)-Net over F₃ — Digital

Digital (158, 227, 475)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(158, 158+69, 10010)-Net in Base 3 — Upper bound on s

There is no (158, 227, 10011)-net in base 3, because

1 times m-reduction [i] would yield (158, 226, 10011)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 676627 651289 712812 286776 434467 313042 776214 243833 236887 412636 069249 960127 193763 878399 928138 775481 445953 063701 > 3²²⁶ [i]