MinT - Best Known (240−107, 240, s)-Nets in Base 3

Best Known (240−107, 240, s)-Nets in Base 3

(240−107, 240, 128)-Net over F₃ — Constructive and digital

Digital (133, 240, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 120, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(240−107, 240, 162)-Net over F₃ — Digital

Digital (133, 240, 162)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−107, 240, 1408)-Net in Base 3 — Upper bound on s

There is no (133, 240, 1409)-net in base 3, because

1 times m-reduction [i] would yield (133, 239, 1409)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 111336 847329 779366 194391 162191 194220 834370 723504 835562 161090 943430 246664 101464 821236 298373 786951 782175 946832 376115 > 3²³⁹ [i]