MinT - Best Known (91, 168, s)-Nets in Base 3

Best Known (91, 168, s)-Nets in Base 3

(91, 168, 73)-Net over F₃ — Constructive and digital

Digital (91, 168, 73)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (26, 64, 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 (27, 104, 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]

(91, 168, 110)-Net over F₃ — Digital

Digital (91, 168, 110)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 168, 901)-Net in Base 3 — Upper bound on s

There is no (91, 168, 902)-net in base 3, because

1 times m-reduction [i] would yield (91, 167, 902)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47 857169 056922 818765 585442 279633 456668 934190 824515 052054 518160 244278 000748 178965 > 3¹⁶⁷ [i]