MinT - Best Known (190, 190+54, s)-Nets in Base 3

Best Known (190, 190+54, s)-Nets in Base 3

(190, 190+54, 688)-Net over F₃ — Constructive and digital

Digital (190, 244, 688)-net over F₃, using

trace code for nets [i] based on digital (7, 61, 172)-net over F₈₁, using
- net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]

(190, 190+54, 1645)-Net over F₃ — Digital

Digital (190, 244, 1645)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(190, 190+54, 111953)-Net in Base 3 — Upper bound on s

There is no (190, 244, 111954)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 261 620444 971669 736713 930165 709720 798522 452248 384847 411661 914509 544228 839999 653769 441529 650072 928366 528272 681601 741473 > 3²⁴⁴ [i]