MinT - Best Known (150−53, 150, s)-Nets in Base 3

Best Known (150−53, 150, s)-Nets in Base 3

(150−53, 150, 156)-Net over F₃ — Constructive and digital

Digital (97, 150, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 75, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(150−53, 150, 209)-Net over F₃ — Digital

Digital (97, 150, 209)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−53, 150, 2835)-Net in Base 3 — Upper bound on s

There is no (97, 150, 2836)-net in base 3, because

1 times m-reduction [i] would yield (97, 149, 2836)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 123658 875029 074607 621483 911383 829684 285811 174937 790917 856311 679457 384217 > 3¹⁴⁹ [i]