MinT - Best Known (198−94, 198, s)-Nets in Base 3

Best Known (198−94, 198, s)-Nets in Base 3

(198−94, 198, 74)-Net over F₃ — Constructive and digital

Digital (104, 198, 74)-net over F₃, using

6 times m-reduction [i] based on digital (104, 204, 74)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (27, 77, 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, 127, 37)-net over F₃, using
    - net from sequence [i] based on digital (27, 36)-sequence over F₃ (see above)

(198−94, 198, 115)-Net over F₃ — Digital

Digital (104, 198, 115)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−94, 198, 894)-Net in Base 3 — Upper bound on s

There is no (104, 198, 895)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 30552 547500 361833 893455 916596 493482 998740 803421 142599 506157 430101 877657 629605 373614 105497 103779 > 3¹⁹⁸ [i]