MinT - Best Known (213−93, 213, s)-Nets in Base 3

Best Known (213−93, 213, s)-Nets in Base 3

(213−93, 213, 128)-Net over F₃ — Constructive and digital

Digital (120, 213, 128)-net over F₃, using

1 times m-reduction [i] based on digital (120, 214, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 107, 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]

(213−93, 213, 154)-Net over F₃ — Digital

Digital (120, 213, 154)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−93, 213, 1377)-Net in Base 3 — Upper bound on s

There is no (120, 213, 1378)-net in base 3, because

1 times m-reduction [i] would yield (120, 212, 1378)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 142193 490577 737670 390902 380948 322201 596498 753405 850099 339046 506897 513647 596602 407881 639215 162616 652301 > 3²¹² [i]