MinT - Best Known (121, 121+41, s)-Nets in Base 3

Best Known (121, 121+41, s)-Nets in Base 3

(121, 121+41, 288)-Net over F₃ — Constructive and digital

Digital (121, 162, 288)-net over F₃, using

3 times m-reduction [i] based on digital (121, 165, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 55, 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]

(121, 121+41, 684)-Net over F₃ — Digital

Digital (121, 162, 684)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(121, 121+41, 28761)-Net in Base 3 — Upper bound on s

There is no (121, 162, 28762)-net in base 3, because

1 times m-reduction [i] would yield (121, 161, 28762)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 65575 575877 188158 961853 157030 958850 296886 295596 882943 000053 578609 285611 400009 > 3¹⁶¹ [i]