MinT - Best Known (245−101, 245, s)-Nets in Base 3

Best Known (245−101, 245, s)-Nets in Base 3

(245−101, 245, 148)-Net over F₃ — Constructive and digital

Digital (144, 245, 148)-net over F₃, using

t-expansion [i] based on digital (142, 245, 148)-net over F₃, using
- 5 times m-reduction [i] based on digital (142, 250, 148)-net over F₃, using
  - trace code for nets [i] based on digital (17, 125, 74)-net over F₉, using
    - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
        a function field by GarcÃa and Quoos [i]

(245−101, 245, 205)-Net over F₃ — Digital

Digital (144, 245, 205)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−101, 245, 2025)-Net in Base 3 — Upper bound on s

There is no (144, 245, 2026)-net in base 3, because

1 times m-reduction [i] would yield (144, 244, 2026)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 262 708159 659793 763445 052710 385207 767012 995551 365180 823664 984616 609917 356329 178325 381733 258550 210098 001149 308107 952421 > 3²⁴⁴ [i]