MinT - Best Known (168, 168+77, s)-Nets in Base 3

Best Known (168, 168+77, s)-Nets in Base 3

(168, 168+77, 192)-Net over F₃ — Constructive and digital

Digital (168, 245, 192)-net over F₃, using

1 times m-reduction [i] based on digital (168, 246, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 82, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(168, 168+77, 457)-Net over F₃ — Digital

Digital (168, 245, 457)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(168, 168+77, 8660)-Net in Base 3 — Upper bound on s

There is no (168, 245, 8661)-net in base 3, because

1 times m-reduction [i] would yield (168, 244, 8661)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 262 650083 392548 357340 160343 211849 470587 013570 910991 424868 549791 447302 986136 998145 276028 352002 407684 805803 693941 826785 > 3²⁴⁴ [i]