MinT - Best Known (25, 66, s)-Nets in Base 3

Best Known (25, 66, s)-Nets in Base 3

(25, 66, 32)-Net over F₃ — Constructive and digital

Digital (25, 66, 32)-net over F₃, using

t-expansion [i] based on digital (21, 66, 32)-net over F₃, using
- net from sequence [i] based on digital (21, 31)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
    - an explicitly constructive algebraic function field [i]

(25, 66, 36)-Net over F₃ — Digital

Digital (25, 66, 36)-net over F₃, using

net from sequence [i] based on digital (25, 35)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 25 and N(F) ≥ 36, using
  - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(25, 66, 111)-Net in Base 3 — Upper bound on s

There is no (25, 66, 112)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁶⁶, 112, S₃, 41), but
- the linear programming bound shows that MÂ â‰¥ 2 205450 991152 037887 110312 460000 695173 586277 462145 772188 035973 400341 003679 931330 959040 941975 977662 936305 383695 760833 / 59412 964566 920537 132921 376858 809704 483274 406706 974380 628937 872880 712941 577778 621185 > 3⁶⁶ [i]