MinT - Best Known (153−55, 153, s)-Nets in Base 3

Best Known (153−55, 153, s)-Nets in Base 3

(153−55, 153, 148)-Net over F₃ — Constructive and digital

Digital (98, 153, 148)-net over F₃, using

9 times m-reduction [i] based on digital (98, 162, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 81, 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]

(153−55, 153, 202)-Net over F₃ — Digital

Digital (98, 153, 202)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(153−55, 153, 2624)-Net in Base 3 — Upper bound on s

There is no (98, 153, 2625)-net in base 3, because

1 times m-reduction [i] would yield (98, 152, 2625)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 346679 957640 732574 356908 062541 260895 877832 509672 279601 324026 944274 087611 > 3¹⁵² [i]