MinT - Best Known (149−58, 149, s)-Nets in Base 3

Best Known (149−58, 149, s)-Nets in Base 3

(149−58, 149, 128)-Net over F₃ — Constructive and digital

Digital (91, 149, 128)-net over F₃, using

7 times m-reduction [i] based on digital (91, 156, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 78, 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]

(149−58, 149, 157)-Net over F₃ — Digital

Digital (91, 149, 157)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−58, 149, 1621)-Net in Base 3 — Upper bound on s

There is no (91, 149, 1622)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 123773 192644 693021 928690 991237 991872 701491 364918 360553 509247 668609 317077 > 3¹⁴⁹ [i]