MinT - Best Known (100, 171, s)-Nets in Base 3

Best Known (100, 171, s)-Nets in Base 3

(100, 171, 128)-Net over F₃ — Constructive and digital

Digital (100, 171, 128)-net over F₃, using

3 times m-reduction [i] based on digital (100, 174, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 87, 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]

(100, 171, 147)-Net over F₃ — Digital

Digital (100, 171, 147)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 171, 1410)-Net in Base 3 — Upper bound on s

There is no (100, 171, 1411)-net in base 3, because

1 times m-reduction [i] would yield (100, 170, 1411)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1314 862213 455919 084605 268219 244284 114281 458198 530578 770831 601585 589936 001470 617195 > 3¹⁷⁰ [i]