MinT - Best Known (240−103, 240, s)-Nets in Base 3

Best Known (240−103, 240, s)-Nets in Base 3

(240−103, 240, 148)-Net over F₃ — Constructive and digital

Digital (137, 240, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 120, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(240−103, 240, 180)-Net over F₃ — Digital

Digital (137, 240, 180)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−103, 240, 1659)-Net in Base 3 — Upper bound on s

There is no (137, 240, 1660)-net in base 3, because

1 times m-reduction [i] would yield (137, 239, 1660)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 104670 406925 334011 044249 752325 226666 336014 281478 716269 830578 949415 189689 407648 839097 476086 060216 903192 130569 981841 > 3²³⁹ [i]