MinT - Best Known (128, 128+85, s)-Nets in Base 3

Best Known (128, 128+85, s)-Nets in Base 3

(128, 128+85, 148)-Net over F₃ — Constructive and digital

Digital (128, 213, 148)-net over F₃, using

9 times m-reduction [i] based on digital (128, 222, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 111, 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]

(128, 128+85, 199)-Net over F₃ — Digital

Digital (128, 213, 199)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 128+85, 2072)-Net in Base 3 — Upper bound on s

There is no (128, 213, 2073)-net in base 3, because

1 times m-reduction [i] would yield (128, 212, 2073)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 141710 614178 187390 028927 727791 098611 658732 145880 022658 757980 517661 860257 131028 544745 327097 309398 262809 > 3²¹² [i]