MinT - Best Known (181−44, 181, s)-Nets in Base 3

Best Known (181−44, 181, s)-Nets in Base 3

(181−44, 181, 400)-Net over F₃ — Constructive and digital

Digital (137, 181, 400)-net over F₃, using

3¹ times duplication [i] based on digital (136, 180, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 45, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(181−44, 181, 879)-Net over F₃ — Digital

Digital (137, 181, 879)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(181−44, 181, 38105)-Net in Base 3 — Upper bound on s

There is no (137, 181, 38106)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 228 631094 851234 718646 174288 019425 651426 679629 833513 390232 502273 747688 177900 351713 140333 > 3¹⁸¹ [i]