MinT - Best Known (217−61, 217, s)-Nets in Base 3

Best Known (217−61, 217, s)-Nets in Base 3

(217−61, 217, 288)-Net over F₃ — Constructive and digital

Digital (156, 217, 288)-net over F₃, using

3¹ times duplication [i] based on digital (155, 216, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 72, 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]

(217−61, 217, 590)-Net over F₃ — Digital

Digital (156, 217, 590)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−61, 217, 16377)-Net in Base 3 — Upper bound on s

There is no (156, 217, 16378)-net in base 3, because

1 times m-reduction [i] would yield (156, 216, 16378)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 441806 484853 751909 703076 418369 748277 995590 864180 325614 616650 828536 574568 555635 064175 059033 799834 383229 > 3²¹⁶ [i]