MinT - Best Known (197−97, 197, s)-Nets in Base 3

Best Known (197−97, 197, s)-Nets in Base 3

(197−97, 197, 72)-Net over F₃ — Constructive and digital

Digital (100, 197, 72)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (26, 74, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [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 (26, 123, 36)-net over F₃, using
  - net from sequence [i] based on digital (26, 35)-sequence over F₃ (see above)

(197−97, 197, 103)-Net over F₃ — Digital

Digital (100, 197, 103)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−97, 197, 785)-Net in Base 3 — Upper bound on s

There is no (100, 197, 786)-net in base 3, because

1 times m-reduction [i] would yield (100, 196, 786)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3400 687203 124893 558474 829919 148000 514127 201785 278249 765852 284965 821904 544999 642258 425494 086625 > 3¹⁹⁶ [i]