MinT - Best Known (100, 100+86, s)-Nets in Base 3

Best Known (100, 100+86, s)-Nets in Base 3

(100, 100+86, 74)-Net over F₃ — Constructive and digital

Digital (100, 186, 74)-net over F₃, using

6 times m-reduction [i] based on digital (100, 192, 74)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (27, 73, 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 (27, 119, 37)-net over F₃, using
    - net from sequence [i] based on digital (27, 36)-sequence over F₃ (see above)

(100, 100+86, 117)-Net over F₃ — Digital

Digital (100, 186, 117)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 100+86, 936)-Net in Base 3 — Upper bound on s

There is no (100, 186, 937)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 57808 212915 461690 641518 570786 558420 712523 304075 455281 942953 779190 919484 742788 448253 469787 > 3¹⁸⁶ [i]