MinT - Best Known (150, 150+63, s)-Nets in Base 3

Best Known (150, 150+63, s)-Nets in Base 3

(150, 150+63, 252)-Net over F₃ — Constructive and digital

Digital (150, 213, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 71, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(150, 150+63, 490)-Net over F₃ — Digital

Digital (150, 213, 490)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 150+63, 11343)-Net in Base 3 — Upper bound on s

There is no (150, 213, 11344)-net in base 3, because

1 times m-reduction [i] would yield (150, 212, 11344)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 141504 245937 790266 127133 269335 700869 448731 649991 439795 520678 822280 825179 128629 511882 730481 027059 233729 > 3²¹² [i]