MinT - Best Known (199−51, 199, s)-Nets in Base 3

Best Known (199−51, 199, s)-Nets in Base 3

(199−51, 199, 288)-Net over F₃ — Constructive and digital

Digital (148, 199, 288)-net over F₃, using

t-expansion [i] based on digital (147, 199, 288)-net over F₃, using
- 5 times m-reduction [i] based on digital (147, 204, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 68, 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]

(199−51, 199, 768)-Net over F₃ — Digital

Digital (148, 199, 768)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−51, 199, 30552)-Net in Base 3 — Upper bound on s

There is no (148, 199, 30553)-net in base 3, because

1 times m-reduction [i] would yield (148, 198, 30553)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29522 332719 494433 624155 855157 931504 248600 423008 794478 597933 495041 832671 268444 157190 700904 321747 > 3¹⁹⁸ [i]