MinT - Best Known (119, 226, s)-Nets in Base 3

Best Known (119, 226, s)-Nets in Base 3

(119, 226, 80)-Net over F₃ — Constructive and digital

Digital (119, 226, 80)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (21, 74, 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 (45, 152, 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]

(119, 226, 130)-Net over F₃ — Digital

Digital (119, 226, 130)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 226, 1040)-Net in Base 3 — Upper bound on s

There is no (119, 226, 1041)-net in base 3, because

1 times m-reduction [i] would yield (119, 225, 1041)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 228810 150145 884779 268917 366801 681384 820913 959655 621016 176261 428440 179883 068870 111148 187368 114336 083294 987347 > 3²²⁵ [i]