MinT - Best Known (243−70, 243, s)-Nets in Base 3

Best Known (243−70, 243, s)-Nets in Base 3

(243−70, 243, 288)-Net over F₃ — Constructive and digital

Digital (173, 243, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 81, 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]

(243−70, 243, 600)-Net over F₃ — Digital

Digital (173, 243, 600)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−70, 243, 14248)-Net in Base 3 — Upper bound on s

There is no (173, 243, 14249)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 87 295643 907893 152396 114473 314273 415244 517276 821118 048771 953471 615819 077495 089727 454312 964639 779235 837398 539892 174971 > 3²⁴³ [i]