MinT - Best Known (249−67, 249, s)-Nets in Base 3

Best Known (249−67, 249, s)-Nets in Base 3

(249−67, 249, 288)-Net over F₃ — Constructive and digital

Digital (182, 249, 288)-net over F₃, using

t-expansion [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]

(249−67, 249, 775)-Net over F₃ — Digital

Digital (182, 249, 775)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−67, 249, 25316)-Net in Base 3 — Upper bound on s

There is no (182, 249, 25317)-net in base 3, because

1 times m-reduction [i] would yield (182, 248, 25317)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21197 490806 652485 490049 598498 885210 788389 013075 925501 018048 921517 428002 435382 439703 331190 437296 262452 791094 390101 256523 > 3²⁴⁸ [i]