MinT - Best Known (240−67, 240, s)-Nets in Base 3

Best Known (240−67, 240, s)-Nets in Base 3

(240−67, 240, 288)-Net over F₃ — Constructive and digital

Digital (173, 240, 288)-net over F₃, using

3 times m-reduction [i] based on digital (173, 243, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 81, 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]

(240−67, 240, 659)-Net over F₃ — Digital

Digital (173, 240, 659)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−67, 240, 18753)-Net in Base 3 — Upper bound on s

There is no (173, 240, 18754)-net in base 3, because

1 times m-reduction [i] would yield (173, 239, 18754)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 076961 558854 671769 163051 654271 077077 360694 590354 379150 256419 031919 148970 203064 738575 448840 365560 278126 269340 265285 > 3²³⁹ [i]