MinT - Best Known (151, 238, s)-Nets in Base 3

Best Known (151, 238, s)-Nets in Base 3

(151, 238, 162)-Net over F₃ — Constructive and digital

Digital (151, 238, 162)-net over F₃, using

trace code for nets [i] based on digital (32, 119, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(151, 238, 282)-Net over F₃ — Digital

Digital (151, 238, 282)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(151, 238, 3556)-Net in Base 3 — Upper bound on s

There is no (151, 238, 3557)-net in base 3, because

1 times m-reduction [i] would yield (151, 237, 3557)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 120358 534381 717361 307642 138755 259904 158043 653622 611863 274223 427193 627369 886937 258003 613044 119608 036958 464147 241227 > 3²³⁷ [i]