MinT - Best Known (248−65, 248, s)-Nets in Base 3

Best Known (248−65, 248, s)-Nets in Base 3

(248−65, 248, 288)-Net over F₃ — Constructive and digital

Digital (183, 248, 288)-net over F₃, using

t-expansion [i] based on digital (177, 248, 288)-net over F₃, using
- 1 times m-reduction [i] based on digital (177, 249, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 83, 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]

(248−65, 248, 850)-Net over F₃ — Digital

Digital (183, 248, 850)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−65, 248, 30774)-Net in Base 3 — Upper bound on s

There is no (183, 248, 30775)-net in base 3, because

1 times m-reduction [i] would yield (183, 247, 30775)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7068 667644 836999 688013 915369 065869 183925 868069 962506 280990 078645 086124 908554 297098 849961 634456 577968 457492 082209 148353 > 3²⁴⁷ [i]