MinT - Best Known (113, 113+79, s)-Nets in Base 3

Best Known (113, 113+79, s)-Nets in Base 3

(113, 113+79, 148)-Net over F₃ — Constructive and digital

Digital (113, 192, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 96, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(113, 113+79, 166)-Net over F₃ — Digital

Digital (113, 192, 166)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+79, 1633)-Net in Base 3 — Upper bound on s

There is no (113, 192, 1634)-net in base 3, because

1 times m-reduction [i] would yield (113, 191, 1634)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 745560 237850 303578 618460 795834 989229 427543 445077 701578 187799 993345 814938 130619 162932 862889 > 3¹⁹¹ [i]