MinT - Best Known (122−38, 122, s)-Nets in Base 4

Best Known (122−38, 122, s)-Nets in Base 4

(122−38, 122, 240)-Net over F₄ — Constructive and digital

Digital (84, 122, 240)-net over F₄, using

t-expansion [i] based on digital (83, 122, 240)-net over F₄, using
- 1 times m-reduction [i] based on digital (83, 123, 240)-net over F₄, using
  - trace code for nets [i] based on digital (1, 41, 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]

(122−38, 122, 478)-Net over F₄ — Digital

Digital (84, 122, 478)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−38, 122, 19391)-Net in Base 4 — Upper bound on s

There is no (84, 122, 19392)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 28 285161 618465 949757 431079 378964 535147 146343 750465 967037 769186 632995 016013 > 4¹²² [i]