MinT - Best Known (245−75, 245, s)-Nets in Base 3

Best Known (245−75, 245, s)-Nets in Base 3

(245−75, 245, 228)-Net over F₃ — Constructive and digital

Digital (170, 245, 228)-net over F₃, using

1 times m-reduction [i] based on digital (170, 246, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 82, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(245−75, 245, 497)-Net over F₃ — Digital

Digital (170, 245, 497)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−75, 245, 10227)-Net in Base 3 — Upper bound on s

There is no (170, 245, 10228)-net in base 3, because

1 times m-reduction [i] would yield (170, 244, 10228)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 262 293077 673049 740171 228306 349522 748849 983862 371238 961389 399190 717635 347151 901379 760171 230207 169840 858235 942905 521353 > 3²⁴⁴ [i]