MinT - Best Known (123, 123+88, s)-Nets in Base 3

Best Known (123, 123+88, s)-Nets in Base 3

(123, 123+88, 148)-Net over F₃ — Constructive and digital

Digital (123, 211, 148)-net over F₃, using

1 times m-reduction [i] based on digital (123, 212, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 106, 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]

(123, 123+88, 174)-Net over F₃ — Digital

Digital (123, 211, 174)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 123+88, 1631)-Net in Base 3 — Upper bound on s

There is no (123, 211, 1632)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47618 279602 469972 269864 385263 257995 543280 238546 867892 794299 746343 838197 850625 335223 688837 294869 100801 > 3²¹¹ [i]