MinT - Best Known (225−77, 225, s)-Nets in Base 3

Best Known (225−77, 225, s)-Nets in Base 3

(225−77, 225, 162)-Net over F₃ — Constructive and digital

Digital (148, 225, 162)-net over F₃, using

7 times m-reduction [i] based on digital (148, 232, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 116, 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]

(225−77, 225, 325)-Net over F₃ — Digital

Digital (148, 225, 325)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−77, 225, 4841)-Net in Base 3 — Upper bound on s

There is no (148, 225, 4842)-net in base 3, because

1 times m-reduction [i] would yield (148, 224, 4842)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 75592 072716 875832 201433 434278 485081 410544 286044 664032 290328 289091 110057 938315 415281 922206 323785 428611 183213 > 3²²⁴ [i]