MinT - Best Known (161, 161+51, s)-Nets in Base 3

Best Known (161, 161+51, s)-Nets in Base 3

(161, 161+51, 464)-Net over F₃ — Constructive and digital

Digital (161, 212, 464)-net over F₃, using

trace code for nets [i] based on digital (2, 53, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(161, 161+51, 1040)-Net over F₃ — Digital

Digital (161, 212, 1040)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(161, 161+51, 54113)-Net in Base 3 — Upper bound on s

There is no (161, 212, 54114)-net in base 3, because

1 times m-reduction [i] would yield (161, 211, 54114)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47071 577329 732902 191950 596092 197816 299644 730123 057981 326125 456373 415577 784238 727924 580573 126877 890901 > 3²¹¹ [i]