MinT - Best Known (200−85, 200, s)-Nets in Base 3

Best Known (200−85, 200, s)-Nets in Base 3

(200−85, 200, 128)-Net over F₃ — Constructive and digital

Digital (115, 200, 128)-net over F₃, using

4 times m-reduction [i] based on digital (115, 204, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 102, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(200−85, 200, 158)-Net over F₃ — Digital

Digital (115, 200, 158)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(200−85, 200, 1463)-Net in Base 3 — Upper bound on s

There is no (115, 200, 1464)-net in base 3, because

1 times m-reduction [i] would yield (115, 199, 1464)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 89633 946052 948859 974173 969745 437000 769632 704218 447866 735422 359486 736813 718142 791160 573490 264913 > 3¹⁹⁹ [i]