MinT - Best Known (154−49, 154, s)-Nets in Base 3

Best Known (154−49, 154, s)-Nets in Base 3

(154−49, 154, 156)-Net over F₃ — Constructive and digital

Digital (105, 154, 156)-net over F₃, using

12 times m-reduction [i] based on digital (105, 166, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 83, 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]

(154−49, 154, 295)-Net over F₃ — Digital

Digital (105, 154, 295)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(154−49, 154, 5371)-Net in Base 3 — Upper bound on s

There is no (105, 154, 5372)-net in base 3, because

1 times m-reduction [i] would yield (105, 153, 5372)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10 015957 152008 625340 151290 939663 739480 918419 265544 301811 564940 731795 674177 > 3¹⁵³ [i]