MinT - Best Known (170−73, 170, s)-Nets in Base 3

Best Known (170−73, 170, s)-Nets in Base 3

(170−73, 170, 80)-Net over F₃ — Constructive and digital

Digital (97, 170, 80)-net over F₃, using

8 times m-reduction [i] based on digital (97, 178, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 89, 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]

(170−73, 170, 133)-Net over F₃ — Digital

Digital (97, 170, 133)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−73, 170, 1205)-Net in Base 3 — Upper bound on s

There is no (97, 170, 1206)-net in base 3, because

1 times m-reduction [i] would yield (97, 169, 1206)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 439 915297 812468 365063 039354 955792 709538 415522 669487 752815 547064 203771 333182 865737 > 3¹⁶⁹ [i]