MinT - Best Known (122−34, 122, s)-Nets in Base 4

Best Known (122−34, 122, s)-Nets in Base 4

(122−34, 122, 384)-Net over F₄ — Constructive and digital

Digital (88, 122, 384)-net over F₄, using

t-expansion [i] based on digital (87, 122, 384)-net over F₄, using
- 1 times m-reduction [i] based on digital (87, 123, 384)-net over F₄, using
  - trace code for nets [i] based on digital (5, 41, 128)-net over F₆₄, using
    - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
        a function field by SÃ©mirat [i]

(122−34, 122, 387)-Net in Base 4 — Constructive

(88, 122, 387)-net in base 4, using

1 times m-reduction [i] based on (88, 123, 387)-net in base 4, using
- trace code for nets [i] based on (6, 41, 129)-net in base 64, using
  - 1 times m-reduction [i] based on (6, 42, 129)-net in base 64, using
    - base change [i] based on digital (0, 36, 129)-net over F₁₂₈, using
      - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 0 and N(F) ≥ 129, using
        the rational function field F₁₂₈(x) [i]
        Niederreiter sequence [i]

(122−34, 122, 754)-Net over F₄ — Digital

Digital (88, 122, 754)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−34, 122, 50046)-Net in Base 4 — Upper bound on s

There is no (88, 122, 50047)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 28 277127 675683 761174 245988 343859 483623 580373 781588 316994 038655 592055 796510 > 4¹²² [i]