MinT - Best Known (219−63, 219, s)-Nets in Base 3

Best Known (219−63, 219, s)-Nets in Base 3

(219−63, 219, 282)-Net over F₃ — Constructive and digital

Digital (156, 219, 282)-net over F₃, using

trace code for nets [i] based on digital (10, 73, 94)-net over F₂₇, using
- net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
    - a function field by SÃ©mirat [i]

(219−63, 219, 550)-Net over F₃ — Digital

Digital (156, 219, 550)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−63, 219, 14037)-Net in Base 3 — Upper bound on s

There is no (156, 219, 14038)-net in base 3, because

1 times m-reduction [i] would yield (156, 218, 14038)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 102 935061 429083 366014 457044 884178 605778 504473 699868 391033 157289 884721 514626 187181 669130 685648 790055 751145 > 3²¹⁸ [i]