MinT - Best Known (122−39, 122, s)-Nets in Base 4

Best Known (122−39, 122, s)-Nets in Base 4

(122−39, 122, 240)-Net over F₄ — Constructive and digital

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]

(122−39, 122, 430)-Net over F₄ — Digital

Digital (83, 122, 430)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−39, 122, 18025)-Net in Base 4 — Upper bound on s

There is no (83, 122, 18026)-net in base 4, because

1 times m-reduction [i] would yield (83, 121, 18026)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 068233 611024 381326 089389 273117 769369 234114 862732 298483 679503 256706 785464 > 4¹²¹ [i]