MinT - Best Known (168, 168+76, s)-Nets in Base 3

Best Known (168, 168+76, s)-Nets in Base 3

(168, 168+76, 204)-Net over F₃ — Constructive and digital

Digital (168, 244, 204)-net over F₃, using

3¹ times duplication [i] based on digital (167, 243, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 81, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(168, 168+76, 469)-Net over F₃ — Digital

Digital (168, 244, 469)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(168, 168+76, 8660)-Net in Base 3 — Upper bound on s

There is no (168, 244, 8661)-net in base 3, because

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]