MinT - Best Known (152, 152+63, s)-Nets in Base 3

Best Known (152, 152+63, s)-Nets in Base 3

(152, 152+63, 252)-Net over F₃ — Constructive and digital

Digital (152, 215, 252)-net over F₃, using

1 times m-reduction [i] based on digital (152, 216, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 72, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(152, 152+63, 509)-Net over F₃ — Digital

Digital (152, 215, 509)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(152, 152+63, 12178)-Net in Base 3 — Upper bound on s

There is no (152, 215, 12179)-net in base 3, because

1 times m-reduction [i] would yield (152, 214, 12179)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 272059 110062 965329 808917 133093 814933 440818 824254 009540 347803 261452 076801 376374 489624 955152 885939 276819 > 3²¹⁴ [i]