MinT - Best Known (179, 179+70, s)-Nets in Base 3

Best Known (179, 179+70, s)-Nets in Base 3

(179, 179+70, 288)-Net over F₃ — Constructive and digital

Digital (179, 249, 288)-net over F₃, using

t-expansion [i] based on digital (177, 249, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 83, 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]

(179, 179+70, 665)-Net over F₃ — Digital

Digital (179, 249, 665)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(179, 179+70, 17208)-Net in Base 3 — Upper bound on s

There is no (179, 249, 17209)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63632 876661 359267 170852 153306 076759 189585 353783 101226 912290 604711 802251 354664 023788 003507 950640 819075 854812 457112 686139 > 3²⁴⁹ [i]