MinT - Best Known (150, 201, s)-Nets in Base 3

Best Known (150, 201, s)-Nets in Base 3

(150, 201, 288)-Net over F₃ — Constructive and digital

Digital (150, 201, 288)-net over F₃, using

t-expansion [i] based on digital (149, 201, 288)-net over F₃, using
- 6 times m-reduction [i] based on digital (149, 207, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 69, 96)-net over F₂₇, using
    - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
        an explicitly constructive algebraic function field [i]

(150, 201, 805)-Net over F₃ — Digital

Digital (150, 201, 805)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 201, 33361)-Net in Base 3 — Upper bound on s

There is no (150, 201, 33362)-net in base 3, because

1 times m-reduction [i] would yield (150, 200, 33362)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 265689 320033 063411 227026 440742 538053 463433 232834 170377 904035 082761 294425 928632 198491 635382 495541 > 3²⁰⁰ [i]