MinT - Best Known (183, 183+67, s)-Nets in Base 4

Best Known (183, 183+67, s)-Nets in Base 4

(183, 183+67, 531)-Net over F₄ — Constructive and digital

Digital (183, 250, 531)-net over F₄, using

t-expansion [i] based on digital (179, 250, 531)-net over F₄, using
- 8 times m-reduction [i] based on digital (179, 258, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 86, 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]

(183, 183+67, 576)-Net in Base 4 — Constructive

(183, 250, 576)-net in base 4, using

2 times m-reduction [i] based on (183, 252, 576)-net in base 4, using
- trace code for nets [i] based on (15, 84, 192)-net in base 64, using
  - base change [i] based on digital (3, 72, 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]

(183, 183+67, 1642)-Net over F₄ — Digital

Digital (183, 250, 1642)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(183, 183+67, 153099)-Net in Base 4 — Upper bound on s

There is no (183, 250, 153100)-net in base 4, because

1 times m-reduction [i] would yield (183, 249, 153100)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 818510 193967 306808 364036 768125 641848 072951 793389 120095 135593 756189 984442 116192 386094 681779 086281 308556 318218 170405 537232 956937 995704 885978 133771 656528 > 4²⁴⁹ [i]