MinT - Best Known (167−71, 167, s)-Nets in Base 3

Best Known (167−71, 167, s)-Nets in Base 3

(167−71, 167, 80)-Net over F₃ — Constructive and digital

Digital (96, 167, 80)-net over F₃, using

9 times m-reduction [i] based on digital (96, 176, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 88, 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]

(167−71, 167, 135)-Net over F₃ — Digital

Digital (96, 167, 135)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(167−71, 167, 1239)-Net in Base 3 — Upper bound on s

There is no (96, 167, 1240)-net in base 3, because

1 times m-reduction [i] would yield (96, 166, 1240)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16 000244 399198 489574 800857 896636 996677 802659 662486 635383 886740 107286 318720 927457 > 3¹⁶⁶ [i]