MinT - Best Known (110, 110+101, s)-Nets in Base 3

Best Known (110, 110+101, s)-Nets in Base 3

(110, 110+101, 76)-Net over F₃ — Constructive and digital

Digital (110, 211, 76)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (15, 65, 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, 146, 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]

(110, 110+101, 118)-Net over F₃ — Digital

Digital (110, 211, 118)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(110, 110+101, 934)-Net in Base 3 — Upper bound on s

There is no (110, 211, 935)-net in base 3, because

1 times m-reduction [i] would yield (110, 210, 935)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16102 685619 726520 066643 761245 301965 470013 181705 256021 200335 008050 054738 741707 406978 022398 552603 029357 > 3²¹⁰ [i]