MinT - Best Known (108, 108+98, s)-Nets in Base 3

Best Known (108, 108+98, s)-Nets in Base 3

(108, 108+98, 75)-Net over F₃ — Constructive and digital

Digital (108, 206, 75)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (27, 76, 37)-net over F₃, using
  - net from sequence [i] based on digital (27, 36)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 26, N(F)Â =Â 36, and 1 place with degree 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
2. digital (32, 130, 38)-net over F₃, using
  - net from sequence [i] based on digital (32, 37)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 32 and N(F) ≥ 38, using
      - an explicitly constructive algebraic function field [i]

(108, 108+98, 118)-Net over F₃ — Digital

Digital (108, 206, 118)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+98, 921)-Net in Base 3 — Upper bound on s

There is no (108, 206, 922)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 203 020633 983348 913777 042429 814186 850995 289161 393332 370301 598526 061143 683050 404088 646842 682893 678165 > 3²⁰⁶ [i]