MinT - Best Known (107, 107+95, s)-Nets in Base 3

Best Known (107, 107+95, s)-Nets in Base 3

(107, 107+95, 76)-Net over F₃ — Constructive and digital

Digital (107, 202, 76)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (15, 62, 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, 140, 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]

(107, 107+95, 120)-Net over F₃ — Digital

Digital (107, 202, 120)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 107+95, 962)-Net in Base 3 — Upper bound on s

There is no (107, 202, 963)-net in base 3, because

1 times m-reduction [i] would yield (107, 201, 963)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 814886 307103 063159 843603 084236 865697 640144 931273 079082 547845 801491 313165 260415 661434 935185 385907 > 3²⁰¹ [i]