MinT - Best Known (198−55, 198, s)-Nets in Base 3

Best Known (198−55, 198, s)-Nets in Base 3

(198−55, 198, 288)-Net over F₃ — Constructive and digital

Digital (143, 198, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 66, 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]

(198−55, 198, 569)-Net over F₃ — Digital

Digital (143, 198, 569)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−55, 198, 16515)-Net in Base 3 — Upper bound on s

There is no (143, 198, 16516)-net in base 3, because

1 times m-reduction [i] would yield (143, 197, 16516)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9841 139610 026505 610845 566699 387062 332962 858463 983309 371641 367720 513718 637194 315958 423138 616177 > 3¹⁹⁷ [i]