MinT - Best Known (197−96, 197, s)-Nets in Base 3

Best Known (197−96, 197, s)-Nets in Base 3

(197−96, 197, 73)-Net over F₃ — Constructive and digital

Digital (101, 197, 73)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (26, 74, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [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 (27, 123, 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]

(197−96, 197, 106)-Net over F₃ — Digital

Digital (101, 197, 106)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−96, 197, 804)-Net in Base 3 — Upper bound on s

There is no (101, 197, 805)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10060 551223 841074 593241 985456 034768 525070 262003 090643 121079 013772 139619 206296 689441 389502 534977 > 3¹⁹⁷ [i]