MinT - Best Known (147, 147+49, s)-Nets in Base 3

Best Known (147, 147+49, s)-Nets in Base 3

(147, 147+49, 328)-Net over F₃ — Constructive and digital

Digital (147, 196, 328)-net over F₃, using

trace code for nets [i] based on digital (0, 49, 82)-net over F₈₁, using
- net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
    - the rational function field F₈₁(x) [i]
  - Niederreiter sequence [i]

(147, 147+49, 836)-Net over F₃ — Digital

Digital (147, 196, 836)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(147, 147+49, 36869)-Net in Base 3 — Upper bound on s

There is no (147, 196, 36870)-net in base 3, because

1 times m-reduction [i] would yield (147, 195, 36870)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1093 475463 072699 357089 671474 625468 744994 568308 148408 766672 726916 040294 037902 966263 391586 206833 > 3¹⁹⁵ [i]