MinT - Best Known (96, 96+41, s)-Nets in Base 3

Best Known (96, 96+41, s)-Nets in Base 3

(96, 96+41, 192)-Net over F₃ — Constructive and digital

Digital (96, 137, 192)-net over F₃, using

1 times m-reduction [i] based on digital (96, 138, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 46, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(96, 96+41, 325)-Net over F₃ — Digital

Digital (96, 137, 325)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(96, 96+41, 7270)-Net in Base 3 — Upper bound on s

There is no (96, 137, 7271)-net in base 3, because

1 times m-reduction [i] would yield (96, 136, 7271)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 77552 466823 758697 891641 668523 222316 093927 793159 426302 136242 600281 > 3¹³⁶ [i]