MinT - Best Known (219−61, 219, s)-Nets in Base 3

Best Known (219−61, 219, s)-Nets in Base 3

(219−61, 219, 288)-Net over F₃ — Constructive and digital

Digital (158, 219, 288)-net over F₃, using

t-expansion [i] based on digital (157, 219, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 73, 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]

(219−61, 219, 614)-Net over F₃ — Digital

Digital (158, 219, 614)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−61, 219, 17624)-Net in Base 3 — Upper bound on s

There is no (158, 219, 17625)-net in base 3, because

1 times m-reduction [i] would yield (158, 218, 17625)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 103 011870 496506 947823 447213 551658 739337 182655 376821 783441 656418 727739 586306 119786 220391 001851 630840 142761 > 3²¹⁸ [i]