MinT - Best Known (120, 120+109, s)-Nets in Base 3

Best Known (120, 120+109, s)-Nets in Base 3

(120, 120+109, 80)-Net over F₃ — Constructive and digital

Digital (120, 229, 80)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (21, 75, 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, 154, 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]

(120, 120+109, 129)-Net over F₃ — Digital

Digital (120, 229, 129)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 120+109, 1031)-Net in Base 3 — Upper bound on s

There is no (120, 229, 1032)-net in base 3, because

1 times m-reduction [i] would yield (120, 228, 1032)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 210849 497615 520148 056964 175649 915978 589250 629336 063392 628395 204739 140682 114067 310479 027695 359014 423782 541617 > 3²²⁸ [i]