MinT - Best Known (212−98, 212, s)-Nets in Base 3

Best Known (212−98, 212, s)-Nets in Base 3

(212−98, 212, 80)-Net over F₃ — Constructive and digital

Digital (114, 212, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 106, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(212−98, 212, 131)-Net over F₃ — Digital

Digital (114, 212, 131)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−98, 212, 1060)-Net in Base 3 — Upper bound on s

There is no (114, 212, 1061)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 144884 062742 408364 342446 609927 929031 123476 003942 240376 920381 160220 150729 885380 297772 626624 970101 683083 > 3²¹² [i]