MinT - Best Known (240−73, 240, s)-Nets in Base 3

Best Known (240−73, 240, s)-Nets in Base 3

(240−73, 240, 246)-Net over F₃ — Constructive and digital

Digital (167, 240, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 80, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(240−73, 240, 498)-Net over F₃ — Digital

Digital (167, 240, 498)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−73, 240, 10466)-Net in Base 3 — Upper bound on s

There is no (167, 240, 10467)-net in base 3, because

1 times m-reduction [i] would yield (167, 239, 10467)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 078964 272261 471823 715648 888931 211578 192694 050185 567233 416412 220173 496181 089289 100375 128994 784445 077981 890382 938265 > 3²³⁹ [i]