MinT - Best Known (223−49, 223, s)-Nets in Base 3

Best Known (223−49, 223, s)-Nets in Base 3

(223−49, 223, 640)-Net over F₃ — Constructive and digital

Digital (174, 223, 640)-net over F₃, using

t-expansion [i] based on digital (173, 223, 640)-net over F₃, using
- 1 times m-reduction [i] based on digital (173, 224, 640)-net over F₃, using
  - trace code for nets [i] based on digital (5, 56, 160)-net over F₈₁, using
    - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
        a function field by SÃ©mirat [i]

(223−49, 223, 1567)-Net over F₃ — Digital

Digital (174, 223, 1567)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−49, 223, 126947)-Net in Base 3 — Upper bound on s

There is no (174, 223, 126948)-net in base 3, because

1 times m-reduction [i] would yield (174, 222, 126948)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8336 122386 343820 873213 148683 588640 993808 617894 800007 971860 829585 415752 675576 585820 331715 103757 324983 860289 > 3²²² [i]