MinT - Best Known (236−61, 236, s)-Nets in Base 3

Best Known (236−61, 236, s)-Nets in Base 3

(236−61, 236, 288)-Net over F₃ — Constructive and digital

Digital (175, 236, 288)-net over F₃, using

10 times m-reduction [i] based on digital (175, 246, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 82, 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]

(236−61, 236, 857)-Net over F₃ — Digital

Digital (175, 236, 857)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−61, 236, 32871)-Net in Base 3 — Upper bound on s

There is no (175, 236, 32872)-net in base 3, because

1 times m-reduction [i] would yield (175, 235, 32872)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13295 551741 159783 366485 261530 371961 974178 611110 543155 021067 043184 686272 789500 273463 014666 824296 700861 287250 989041 > 3²³⁵ [i]