MinT - Best Known (214−62, 214, s)-Nets in Base 3

Best Known (214−62, 214, s)-Nets in Base 3

(214−62, 214, 264)-Net over F₃ — Constructive and digital

Digital (152, 214, 264)-net over F₃, using

3¹ times duplication [i] based on digital (151, 213, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 71, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(214−62, 214, 526)-Net over F₃ — Digital

Digital (152, 214, 526)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−62, 214, 12178)-Net in Base 3 — Upper bound on s

There is no (152, 214, 12179)-net in base 3, because

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]