MinT - Best Known (130, 130+113, s)-Nets in Base 3

Best Known (130, 130+113, s)-Nets in Base 3

(130, 130+113, 85)-Net over F₃ — Constructive and digital

Digital (130, 243, 85)-net over F₃, using

3 times m-reduction [i] based on digital (130, 246, 85)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (27, 85, 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 (45, 161, 48)-net over F₃, using
    - net from sequence [i] based on digital (45, 47)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
        an explicitly constructive algebraic function field [i]

(130, 130+113, 145)-Net over F₃ — Digital

Digital (130, 243, 145)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(130, 130+113, 1197)-Net in Base 3 — Upper bound on s

There is no (130, 243, 1198)-net in base 3, because

1 times m-reduction [i] would yield (130, 242, 1198)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 30 293093 656535 188338 094095 979018 347771 696596 776371 070901 999454 792509 921157 409071 497827 823492 410271 830782 198930 652209 > 3²⁴² [i]