MinT - Best Known (148, 148+53, s)-Nets in Base 3

Best Known (148, 148+53, s)-Nets in Base 3

(148, 148+53, 288)-Net over F₃ — Constructive and digital

Digital (148, 201, 288)-net over F₃, using

t-expansion [i] based on digital (147, 201, 288)-net over F₃, using
- 3 times m-reduction [i] based on digital (147, 204, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 68, 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]

(148, 148+53, 695)-Net over F₃ — Digital

Digital (148, 201, 695)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(148, 148+53, 24659)-Net in Base 3 — Upper bound on s

There is no (148, 201, 24660)-net in base 3, because

1 times m-reduction [i] would yield (148, 200, 24660)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 265855 689292 837819 993218 592256 159489 006203 226588 204349 409109 370624 706150 287447 362931 700680 371865 > 3²⁰⁰ [i]