MinT - Best Known (195−77, 195, s)-Nets in Base 3

Best Known (195−77, 195, s)-Nets in Base 3

(195−77, 195, 148)-Net over F₃ — Constructive and digital

Digital (118, 195, 148)-net over F₃, using

7 times m-reduction [i] based on digital (118, 202, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 101, 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]

(195−77, 195, 190)-Net over F₃ — Digital

Digital (118, 195, 190)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(195−77, 195, 2012)-Net in Base 3 — Upper bound on s

There is no (118, 195, 2013)-net in base 3, because

1 times m-reduction [i] would yield (118, 194, 2013)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 370 688058 521942 844454 290035 076148 503709 329239 731662 784163 751403 061706 846179 613447 617174 494001 > 3¹⁹⁴ [i]