MinT - Best Known (210−59, 210, s)-Nets in Base 3

Best Known (210−59, 210, s)-Nets in Base 3

(210−59, 210, 288)-Net over F₃ — Constructive and digital

Digital (151, 210, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 70, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(210−59, 210, 575)-Net over F₃ — Digital

Digital (151, 210, 575)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−59, 210, 15991)-Net in Base 3 — Upper bound on s

There is no (151, 210, 15992)-net in base 3, because

1 times m-reduction [i] would yield (151, 209, 15992)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5235 043967 668153 181433 286063 254992 871536 401216 004943 319756 245600 515159 509525 386954 758588 173481 332977 > 3²⁰⁹ [i]