MinT - Best Known (226−65, 226, s)-Nets in Base 3

Best Known (226−65, 226, s)-Nets in Base 3

(226−65, 226, 282)-Net over F₃ — Constructive and digital

Digital (161, 226, 282)-net over F₃, using

3¹ times duplication [i] based on digital (160, 225, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 75, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(226−65, 226, 566)-Net over F₃ — Digital

Digital (161, 226, 566)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−65, 226, 14443)-Net in Base 3 — Upper bound on s

There is no (161, 226, 14444)-net in base 3, because

1 times m-reduction [i] would yield (161, 225, 14444)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 225442 092291 409206 905582 593914 040609 948158 690021 042770 664359 111955 132921 619419 913071 815973 108187 710059 874561 > 3²²⁵ [i]