MinT - Best Known (221−61, 221, s)-Nets in Base 3

Best Known (221−61, 221, s)-Nets in Base 3

(221−61, 221, 288)-Net over F₃ — Constructive and digital

Digital (160, 221, 288)-net over F₃, using

t-expansion [i] based on digital (159, 221, 288)-net over F₃, using
- 1 times m-reduction [i] based on digital (159, 222, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 74, 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]

(221−61, 221, 639)-Net over F₃ — Digital

Digital (160, 221, 639)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−61, 221, 18965)-Net in Base 3 — Upper bound on s

There is no (160, 221, 18966)-net in base 3, because

1 times m-reduction [i] would yield (160, 220, 18966)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 926 293379 986938 559706 612402 622305 909190 473800 478478 432451 309541 228054 499014 136696 522740 915181 433209 053541 > 3²²⁰ [i]