MinT - Best Known (236−81, 236, s)-Nets in Base 3

Best Known (236−81, 236, s)-Nets in Base 3

(236−81, 236, 162)-Net over F₃ — Constructive and digital

Digital (155, 236, 162)-net over F₃, using

10 times m-reduction [i] based on digital (155, 246, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 123, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(236−81, 236, 336)-Net over F₃ — Digital

Digital (155, 236, 336)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−81, 236, 4970)-Net in Base 3 — Upper bound on s

There is no (155, 236, 4971)-net in base 3, because

1 times m-reduction [i] would yield (155, 235, 4971)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13315 225658 277212 189948 736094 505270 037622 646070 461005 065353 102018 565194 731205 190320 605030 211047 063358 916386 224689 > 3²³⁵ [i]