MinT - Best Known (247−91, 247, s)-Nets in Base 3

Best Known (247−91, 247, s)-Nets in Base 3

(247−91, 247, 162)-Net over F₃ — Constructive and digital

Digital (156, 247, 162)-net over F₃, using

1 times m-reduction [i] based on digital (156, 248, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 124, 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]

(247−91, 247, 285)-Net over F₃ — Digital

Digital (156, 247, 285)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−91, 247, 3531)-Net in Base 3 — Upper bound on s

There is no (156, 247, 3532)-net in base 3, because

1 times m-reduction [i] would yield (156, 246, 3532)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2359 955705 097635 017899 300086 942732 425975 470701 514050 554410 181958 605356 078212 064079 382101 335740 626400 527476 594029 150585 > 3²⁴⁶ [i]