MinT - Best Known (148−53, 148, s)-Nets in Base 3

Best Known (148−53, 148, s)-Nets in Base 3

(148−53, 148, 148)-Net over F₃ — Constructive and digital

Digital (95, 148, 148)-net over F₃, using

8 times m-reduction [i] based on digital (95, 156, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 78, 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]

(148−53, 148, 199)-Net over F₃ — Digital

Digital (95, 148, 199)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−53, 148, 2603)-Net in Base 3 — Upper bound on s

There is no (95, 148, 2604)-net in base 3, because

1 times m-reduction [i] would yield (95, 147, 2604)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13722 138259 609560 099959 486648 720555 831087 266049 647460 260334 441000 693289 > 3¹⁴⁷ [i]