MinT - Best Known (226−63, 226, s)-Nets in Base 3

Best Known (226−63, 226, s)-Nets in Base 3

(226−63, 226, 288)-Net over F₃ — Constructive and digital

Digital (163, 226, 288)-net over F₃, using

2 times m-reduction [i] based on digital (163, 228, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 76, 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]

(226−63, 226, 629)-Net over F₃ — Digital

Digital (163, 226, 629)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−63, 226, 17998)-Net in Base 3 — Upper bound on s

There is no (163, 226, 17999)-net in base 3, because

1 times m-reduction [i] would yield (163, 225, 17999)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 225105 538784 486822 131087 931916 629357 291329 332526 942095 654285 409670 411286 185502 399372 129697 459800 543361 533699 > 3²²⁵ [i]