MinT - Best Known (212−93, 212, s)-Nets in Base 3

Best Known (212−93, 212, s)-Nets in Base 3

(212−93, 212, 128)-Net over F₃ — Constructive and digital

Digital (119, 212, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 106, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(212−93, 212, 152)-Net over F₃ — Digital

Digital (119, 212, 152)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−93, 212, 1344)-Net in Base 3 — Upper bound on s

There is no (119, 212, 1345)-net in base 3, because

1 times m-reduction [i] would yield (119, 211, 1345)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 48295 086861 759476 034881 161453 348871 459157 917987 863875 522923 943825 948234 523866 259203 956557 453790 690937 > 3²¹¹ [i]