MinT - Best Known (182−82, 182, s)-Nets in Base 3

Best Known (182−82, 182, s)-Nets in Base 3

(182−82, 182, 80)-Net over F₃ — Constructive and digital

Digital (100, 182, 80)-net over F₃, using

2 times m-reduction [i] based on digital (100, 184, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 92, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(182−82, 182, 123)-Net over F₃ — Digital

Digital (100, 182, 123)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−82, 182, 1018)-Net in Base 3 — Upper bound on s

There is no (100, 182, 1019)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 685 955541 063240 683461 121239 593795 146567 633994 980153 092533 877853 613022 613377 175200 216935 > 3¹⁸² [i]