MinT - Best Known (201−56, 201, s)-Nets in Base 3

Best Known (201−56, 201, s)-Nets in Base 3

(201−56, 201, 288)-Net over F₃ — Constructive and digital

Digital (145, 201, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 67, 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]

(201−56, 201, 570)-Net over F₃ — Digital

Digital (145, 201, 570)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(201−56, 201, 15004)-Net in Base 3 — Upper bound on s

There is no (145, 201, 15005)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 797179 299829 131010 062607 889772 118853 091636 428415 257541 453082 653618 892823 870907 966554 776387 144113 > 3²⁰¹ [i]