MinT - Best Known (241−86, 241, s)-Nets in Base 3

Best Known (241−86, 241, s)-Nets in Base 3

(241−86, 241, 162)-Net over F₃ — Constructive and digital

Digital (155, 241, 162)-net over F₃, using

5 times m-reduction [i] based on digital (155, 246, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 123, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(241−86, 241, 305)-Net over F₃ — Digital

Digital (155, 241, 305)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−86, 241, 3943)-Net in Base 3 — Upper bound on s

There is no (155, 241, 3944)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 720938 935908 480910 933214 885037 595735 081110 710263 829522 507578 743519 613149 953182 200984 246879 449125 970277 754217 778465 > 3²⁴¹ [i]