MinT - Best Known (152, 152+65, s)-Nets in Base 3

Best Known (152, 152+65, s)-Nets in Base 3

(152, 152+65, 246)-Net over F₃ — Constructive and digital

Digital (152, 217, 246)-net over F₃, using

3¹ times duplication [i] based on digital (151, 216, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 72, 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]

(152, 152+65, 478)-Net over F₃ — Digital

Digital (152, 217, 478)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(152, 152+65, 10595)-Net in Base 3 — Upper bound on s

There is no (152, 217, 10596)-net in base 3, because

1 times m-reduction [i] would yield (152, 216, 10596)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 442813 449301 048420 445094 029031 872725 785571 451873 473192 020734 618600 713676 278493 505982 476425 356024 392961 > 3²¹⁶ [i]