MinT - Best Known (108−37, 108, s)-Nets in Base 3

Best Known (108−37, 108, s)-Nets in Base 3

(108−37, 108, 148)-Net over F₃ — Constructive and digital

Digital (71, 108, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 54, 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]

(108−37, 108, 176)-Net over F₃ — Digital

Digital (71, 108, 176)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(108−37, 108, 2572)-Net in Base 3 — Upper bound on s

There is no (71, 108, 2573)-net in base 3, because

1 times m-reduction [i] would yield (71, 107, 2573)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1129 678422 171023 402207 722042 257029 292500 044607 656161 > 3¹⁰⁷ [i]