MinT - Best Known (202−47, 202, s)-Nets in Base 3

Best Known (202−47, 202, s)-Nets in Base 3

(202−47, 202, 464)-Net over F₃ — Constructive and digital

Digital (155, 202, 464)-net over F₃, using

2 times m-reduction [i] based on digital (155, 204, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 51, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(202−47, 202, 1143)-Net over F₃ — Digital

Digital (155, 202, 1143)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−47, 202, 69648)-Net in Base 3 — Upper bound on s

There is no (155, 202, 69649)-net in base 3, because

1 times m-reduction [i] would yield (155, 201, 69649)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 797009 935127 429205 013889 388620 705631 487072 217012 586578 605011 823197 659576 816218 259329 961222 690955 > 3²⁰¹ [i]