MinT - Best Known (106−32, 106, s)-Nets in Base 3

Best Known (106−32, 106, s)-Nets in Base 3

(106−32, 106, 156)-Net over F₃ — Constructive and digital

Digital (74, 106, 156)-net over F₃, using

3¹ times duplication [i] based on digital (73, 105, 156)-net over F₃, using
- trace code for nets [i] based on digital (3, 35, 52)-net over F₂₇, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by SÃ©mirat [i]

(106−32, 106, 259)-Net over F₃ — Digital

Digital (74, 106, 259)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−32, 106, 4909)-Net in Base 3 — Upper bound on s

There is no (74, 106, 4910)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 375 869199 333843 771617 370837 248101 658876 100346 889121 > 3¹⁰⁶ [i]