MinT - Best Known (100, 159, s)-Nets in Base 3

Best Known (100, 159, s)-Nets in Base 3

(100, 159, 148)-Net over F₃ — Constructive and digital

Digital (100, 159, 148)-net over F₃, using

7 times m-reduction [i] based on digital (100, 166, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 83, 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]

(100, 159, 190)-Net over F₃ — Digital

Digital (100, 159, 190)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 159, 2292)-Net in Base 3 — Upper bound on s

There is no (100, 159, 2293)-net in base 3, because

1 times m-reduction [i] would yield (100, 158, 2293)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2453 776477 716536 167271 824841 640245 818687 946147 351593 432963 687943 180513 770395 > 3¹⁵⁸ [i]