MinT - Best Known (239−87, 239, s)-Nets in Base 3

Best Known (239−87, 239, s)-Nets in Base 3

(239−87, 239, 162)-Net over F₃ — Constructive and digital

Digital (152, 239, 162)-net over F₃, using

1 times m-reduction [i] based on digital (152, 240, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 120, 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]

(239−87, 239, 286)-Net over F₃ — Digital

Digital (152, 239, 286)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−87, 239, 3649)-Net in Base 3 — Upper bound on s

There is no (152, 239, 3650)-net in base 3, because

1 times m-reduction [i] would yield (152, 238, 3650)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 360494 344169 043527 096091 956913 313010 303124 963540 601310 034205 919930 637214 549586 983942 824116 604356 091371 589037 255233 > 3²³⁸ [i]