MinT - Best Known (198−95, 198, s)-Nets in Base 3

Best Known (198−95, 198, s)-Nets in Base 3

(198−95, 198, 74)-Net over F₃ — Constructive and digital

Digital (103, 198, 74)-net over F₃, using

3 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)

(198−95, 198, 111)-Net over F₃ — Digital

Digital (103, 198, 111)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−95, 198, 872)-Net in Base 3 — Upper bound on s

There is no (103, 198, 873)-net in base 3, because

1 times m-reduction [i] would yield (103, 197, 873)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10033 562859 733594 086111 543224 253395 527641 876483 959209 015397 739449 219127 031566 063324 995546 617227 > 3¹⁹⁷ [i]