MinT - Best Known (149, 149+55, s)-Nets in Base 4

Best Known (149, 149+55, s)-Nets in Base 4

(149, 149+55, 531)-Net over F₄ — Constructive and digital

Digital (149, 204, 531)-net over F₄, using

9 times m-reduction [i] based on digital (149, 213, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 71, 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]

(149, 149+55, 576)-Net in Base 4 — Constructive

(149, 204, 576)-net in base 4, using

trace code for nets [i] based on (13, 68, 192)-net in base 64, using
- 2 times m-reduction [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]

(149, 149+55, 1342)-Net over F₄ — Digital

Digital (149, 204, 1342)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(149, 149+55, 122407)-Net in Base 4 — Upper bound on s

There is no (149, 204, 122408)-net in base 4, because

1 times m-reduction [i] would yield (149, 203, 122408)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 165 296202 795684 485520 752410 023917 368415 483298 987841 652638 700753 189922 439297 806403 330028 340432 117562 618751 042454 332678 567236 > 4²⁰³ [i]