MinT - Best Known (184−64, 184, s)-Nets in Base 3

Best Known (184−64, 184, s)-Nets in Base 3

(184−64, 184, 156)-Net over F₃ — Constructive and digital

Digital (120, 184, 156)-net over F₃, using

12 times m-reduction [i] based on digital (120, 196, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 98, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(184−64, 184, 260)-Net over F₃ — Digital

Digital (120, 184, 260)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(184−64, 184, 3511)-Net in Base 3 — Upper bound on s

There is no (120, 184, 3512)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6225 431739 853236 854935 099511 092979 811102 216756 382205 559659 555973 024444 469777 397746 042881 > 3¹⁸⁴ [i]