MinT - Best Known (208−63, 208, s)-Nets in Base 3

Best Known (208−63, 208, s)-Nets in Base 3

(208−63, 208, 228)-Net over F₃ — Constructive and digital

Digital (145, 208, 228)-net over F₃, using

3¹ times duplication [i] based on digital (144, 207, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 69, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(208−63, 208, 445)-Net over F₃ — Digital

Digital (145, 208, 445)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−63, 208, 9496)-Net in Base 3 — Upper bound on s

There is no (145, 208, 9497)-net in base 3, because

1 times m-reduction [i] would yield (145, 207, 9497)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 582 368966 410629 660451 567807 516110 959678 937146 652692 366688 375910 385584 829037 248575 989818 640762 961035 > 3²⁰⁷ [i]