MinT - Best Known (154, 154+60, s)-Nets in Base 3

Best Known (154, 154+60, s)-Nets in Base 3

(154, 154+60, 288)-Net over F₃ — Constructive and digital

Digital (154, 214, 288)-net over F₃, using

3¹ times duplication [i] based on digital (153, 213, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 71, 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]

(154, 154+60, 588)-Net over F₃ — Digital

Digital (154, 214, 588)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(154, 154+60, 15218)-Net in Base 3 — Upper bound on s

There is no (154, 214, 15219)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 270671 122027 596579 608787 478628 840814 817879 196092 389819 253516 294769 780583 583394 321469 189607 805553 847821 > 3²¹⁴ [i]