MinT - Best Known (93, 93+90, s)-Nets in Base 3

Best Known (93, 93+90, s)-Nets in Base 3

(93, 93+90, 69)-Net over F₃ — Constructive and digital

Digital (93, 183, 69)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. 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]
2. digital (27, 117, 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]

(93, 93+90, 97)-Net over F₃ — Digital

Digital (93, 183, 97)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(93, 93+90, 724)-Net in Base 3 — Upper bound on s

There is no (93, 183, 725)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2096 272617 375295 376857 163794 001019 315785 435374 223044 805650 153957 530382 230331 073162 816539 > 3¹⁸³ [i]