MinT - Best Known (163−43, 163, s)-Nets in Base 3

Best Known (163−43, 163, s)-Nets in Base 3

(163−43, 163, 288)-Net over F₃ — Constructive and digital

Digital (120, 163, 288)-net over F₃, using

3¹ times duplication [i] based on digital (119, 162, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 54, 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]

(163−43, 163, 585)-Net over F₃ — Digital

Digital (120, 163, 585)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−43, 163, 20781)-Net in Base 3 — Upper bound on s

There is no (120, 163, 20782)-net in base 3, because

1 times m-reduction [i] would yield (120, 162, 20782)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 196656 559960 719046 425373 643864 642228 115502 392440 865522 367869 024625 300202 437845 > 3¹⁶² [i]