MinT - Best Known (153, 153+56, s)-Nets in Base 4

Best Known (153, 153+56, s)-Nets in Base 4

(153, 153+56, 531)-Net over F₄ — Constructive and digital

Digital (153, 209, 531)-net over F₄, using

10 times m-reduction [i] based on digital (153, 219, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 73, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(153, 153+56, 576)-Net in Base 4 — Constructive

(153, 209, 576)-net in base 4, using

1 times m-reduction [i] based on (153, 210, 576)-net in base 4, using
- trace code for nets [i] based on (13, 70, 192)-net in base 64, using
  - base change [i] based on digital (3, 60, 192)-net over F₁₂₈, using
    - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(153, 153+56, 1407)-Net over F₄ — Digital

Digital (153, 209, 1407)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(153, 153+56, 117421)-Net in Base 4 — Upper bound on s

There is no (153, 209, 117422)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 677023 555037 155929 736780 487527 810223 929217 347235 068875 598854 942723 935534 265808 092597 884245 731694 223356 022205 736516 575864 393466 > 4²⁰⁹ [i]