MinT - Best Known (199−96, 199, s)-Nets in Base 3

Best Known (199−96, 199, s)-Nets in Base 3

(199−96, 199, 74)-Net over F₃ — Constructive and digital

Digital (103, 199, 74)-net over F₃, using

2 times m-reduction [i] based on digital (103, 201, 74)-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 (27, 125, 37)-net over F₃, using
    - net from sequence [i] based on digital (27, 36)-sequence over F₃ (see above)

(199−96, 199, 110)-Net over F₃ — Digital

Digital (103, 199, 110)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−96, 199, 844)-Net in Base 3 — Upper bound on s

There is no (103, 199, 845)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 91360 159069 238618 373536 849432 470469 624271 369136 089411 568715 870621 424404 651033 487621 675100 018497 > 3¹⁹⁹ [i]