MinT - Best Known (250−66, 250, s)-Nets in Base 4

Best Known (250−66, 250, s)-Nets in Base 4

(250−66, 250, 531)-Net over F₄ — Constructive and digital

Digital (184, 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]

(250−66, 250, 648)-Net in Base 4 — Constructive

(184, 250, 648)-net in base 4, using

4¹ times duplication [i] based on (183, 249, 648)-net in base 4, using
- trace code for nets [i] based on (17, 83, 216)-net in base 64, using
  - 1 times m-reduction [i] based on (17, 84, 216)-net in base 64, using
    - base change [i] based on digital (5, 72, 216)-net over F₁₂₈, using
      - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(250−66, 250, 1759)-Net over F₄ — Digital

Digital (184, 250, 1759)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−66, 250, 159668)-Net in Base 4 — Upper bound on s

There is no (184, 250, 159669)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 273548 830345 737850 761387 506803 851712 214047 421031 341271 688627 345842 096378 510363 903423 793175 130638 456736 729505 224602 619463 909530 418323 439929 842068 562752 > 4²⁵⁰ [i]