MinT - Best Known (220−59, 220, s)-Nets in Base 3

Best Known (220−59, 220, s)-Nets in Base 3

(220−59, 220, 288)-Net over F₃ — Constructive and digital

Digital (161, 220, 288)-net over F₃, using

5 times m-reduction [i] based on digital (161, 225, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 75, 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]

(220−59, 220, 705)-Net over F₃ — Digital

Digital (161, 220, 705)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−59, 220, 23369)-Net in Base 3 — Upper bound on s

There is no (161, 220, 23370)-net in base 3, because

1 times m-reduction [i] would yield (161, 219, 23370)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 308 870012 896955 559427 885348 410892 864698 497933 778160 780208 970903 200265 666441 856002 124298 079440 068063 985021 > 3²¹⁹ [i]