MinT - Best Known (161, 161+70, s)-Nets in Base 3

Best Known (161, 161+70, s)-Nets in Base 3

(161, 161+70, 246)-Net over F₃ — Constructive and digital

Digital (161, 231, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 77, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(161, 161+70, 487)-Net over F₃ — Digital

Digital (161, 231, 487)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(161, 161+70, 9765)-Net in Base 3 — Upper bound on s

There is no (161, 231, 9766)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 164 220292 207720 672377 898288 796465 748713 657407 927472 534874 251777 563130 759887 370578 388381 016263 676651 298816 881441 > 3²³¹ [i]