MinT - Best Known (157−45, 157, s)-Nets in Base 3

Best Known (157−45, 157, s)-Nets in Base 3

(157−45, 157, 246)-Net over F₃ — Constructive and digital

Digital (112, 157, 246)-net over F₃, using

3¹ times duplication [i] based on digital (111, 156, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 52, 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]

(157−45, 157, 420)-Net over F₃ — Digital

Digital (112, 157, 420)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−45, 157, 10919)-Net in Base 3 — Upper bound on s

There is no (112, 157, 10920)-net in base 3, because

1 times m-reduction [i] would yield (112, 156, 10920)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 270 127574 503872 671839 656154 422569 657321 260214 227760 923107 581846 025376 266993 > 3¹⁵⁶ [i]