MinT - Best Known (216−41, 216, s)-Nets in Base 3

Best Known (216−41, 216, s)-Nets in Base 3

(216−41, 216, 896)-Net over F₃ — Constructive and digital

Digital (175, 216, 896)-net over F₃, using

trace code for nets [i] based on digital (13, 54, 224)-net over F₈₁, using
- net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
    - a function field by SÃ©mirat [i]

(216−41, 216, 2993)-Net over F₃ — Digital

Digital (175, 216, 2993)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−41, 216, 558874)-Net in Base 3 — Upper bound on s

There is no (175, 216, 558875)-net in base 3, because

1 times m-reduction [i] would yield (175, 215, 558875)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 811290 111936 123703 587372 817684 435494 094502 912362 630802 102521 527093 680094 123602 479523 153850 842009 238201 > 3²¹⁵ [i]