MinT - Best Known (200−50, 200, s)-Nets in Base 3

Best Known (200−50, 200, s)-Nets in Base 3

(200−50, 200, 328)-Net over F₃ — Constructive and digital

Digital (150, 200, 328)-net over F₃, using

trace code for nets [i] based on digital (0, 50, 82)-net over F₈₁, using
- net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
    - the rational function field F₈₁(x) [i]
  - Niederreiter sequence [i]

(200−50, 200, 850)-Net over F₃ — Digital

Digital (150, 200, 850)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(200−50, 200, 33361)-Net in Base 3 — Upper bound on s

There is no (150, 200, 33362)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 265689 320033 063411 227026 440742 538053 463433 232834 170377 904035 082761 294425 928632 198491 635382 495541 > 3²⁰⁰ [i]