MinT - Best Known (108, 108+75, s)-Nets in Base 3

Best Known (108, 108+75, s)-Nets in Base 3

(108, 108+75, 128)-Net over F₃ — Constructive and digital

Digital (108, 183, 128)-net over F₃, using

7 times m-reduction [i] based on digital (108, 190, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 95, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(108, 108+75, 161)-Net over F₃ — Digital

Digital (108, 183, 161)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+75, 1592)-Net in Base 3 — Upper bound on s

There is no (108, 183, 1593)-net in base 3, because

1 times m-reduction [i] would yield (108, 182, 1593)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 695 117186 372848 272674 480295 103366 516648 612276 369529 264651 824103 758957 944762 630178 652771 > 3¹⁸² [i]