MinT - Best Known (96, 96+37, s)-Nets in Base 3

Best Known (96, 96+37, s)-Nets in Base 3

(96, 96+37, 246)-Net over F₃ — Constructive and digital

Digital (96, 133, 246)-net over F₃, using

3¹ times duplication [i] based on digital (95, 132, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 44, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(96, 96+37, 410)-Net over F₃ — Digital

Digital (96, 133, 410)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(96, 96+37, 11894)-Net in Base 3 — Upper bound on s

There is no (96, 133, 11895)-net in base 3, because

1 times m-reduction [i] would yield (96, 132, 11895)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 955 529919 757445 327681 409089 317411 808317 184974 061016 268185 050445 > 3¹³² [i]