MinT - Best Known (116, 116+113, s)-Nets in Base 3

Best Known (116, 116+113, s)-Nets in Base 3

(116, 116+113, 76)-Net over F₃ — Constructive and digital

Digital (116, 229, 76)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (15, 71, 28)-net over F₃, using
  - net from sequence [i] based on digital (15, 27)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
      - an explicitly constructive algebraic function field [i]
2. digital (45, 158, 48)-net over F₃, using
  - net from sequence [i] based on digital (45, 47)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
      - an explicitly constructive algebraic function field [i]

(116, 116+113, 120)-Net over F₃ — Digital

Digital (116, 229, 120)-net over F₃, using

t-expansion [i] based on digital (113, 229, 120)-net over F₃, using
- net from sequence [i] based on digital (113, 119)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 113 and N(F) ≥ 120, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(116, 116+113, 896)-Net in Base 3 — Upper bound on s

There is no (116, 229, 897)-net in base 3, because

1 times m-reduction [i] would yield (116, 228, 897)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 149304 658916 522917 865559 778251 987254 477351 493001 087919 273989 797068 139589 591048 930229 753992 203543 161382 119265 > 3²²⁸ [i]