MinT - Best Known (242−82, 242, s)-Nets in Base 3

Best Known (242−82, 242, s)-Nets in Base 3

(242−82, 242, 162)-Net over F₃ — Constructive and digital

Digital (160, 242, 162)-net over F₃, using

t-expansion [i] based on digital (157, 242, 162)-net over F₃, using
- 8 times m-reduction [i] based on digital (157, 250, 162)-net over F₃, using
  - trace code for nets [i] based on digital (32, 125, 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]

(242−82, 242, 357)-Net over F₃ — Digital

Digital (160, 242, 357)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−82, 242, 5244)-Net in Base 3 — Upper bound on s

There is no (160, 242, 5245)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 100158 605915 678626 362514 667278 261214 241640 884999 837378 303033 980161 687731 639039 960651 409221 541378 226246 638560 401755 > 3²⁴² [i]