MinT - Best Known (85, 85+62, s)-Nets in Base 3

Best Known (85, 85+62, s)-Nets in Base 3

(85, 85+62, 80)-Net over F₃ — Constructive and digital

Digital (85, 147, 80)-net over F₃, using

7 times m-reduction [i] based on digital (85, 154, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 77, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(85, 85+62, 124)-Net over F₃ — Digital

Digital (85, 147, 124)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+62, 1106)-Net in Base 3 — Upper bound on s

There is no (85, 147, 1107)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 14041 550666 562840 341359 722568 533227 720787 792002 205791 577278 803772 536595 > 3¹⁴⁷ [i]