MinT - Best Known (200−61, 200, s)-Nets in Base 3

Best Known (200−61, 200, s)-Nets in Base 3

(200−61, 200, 204)-Net over F₃ — Constructive and digital

Digital (139, 200, 204)-net over F₃, using

1 times m-reduction [i] based on digital (139, 201, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 67, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(200−61, 200, 420)-Net over F₃ — Digital

Digital (139, 200, 420)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(200−61, 200, 8774)-Net in Base 3 — Upper bound on s

There is no (139, 200, 8775)-net in base 3, because

1 times m-reduction [i] would yield (139, 199, 8775)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 88780 935085 488771 690296 983941 520395 044731 232767 951549 101675 121571 847293 460143 335689 420842 499093 > 3¹⁹⁹ [i]