MinT - Best Known (106−33, 106, s)-Nets in Base 4

Best Known (106−33, 106, s)-Nets in Base 4

(106−33, 106, 240)-Net over F₄ — Constructive and digital

Digital (73, 106, 240)-net over F₄, using

2 times m-reduction [i] based on digital (73, 108, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 36, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(106−33, 106, 432)-Net over F₄ — Digital

Digital (73, 106, 432)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−33, 106, 20237)-Net in Base 4 — Upper bound on s

There is no (73, 106, 20238)-net in base 4, because

1 times m-reduction [i] would yield (73, 105, 20238)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1645 908880 619890 392491 374456 442057 559636 733984 260038 137450 315120 > 4¹⁰⁵ [i]