MinT - Best Known (220−67, 220, s)-Nets in Base 4

Best Known (220−67, 220, s)-Nets in Base 4

(220−67, 220, 450)-Net over F₄ — Constructive and digital

Digital (153, 220, 450)-net over F₄, using

6 times m-reduction [i] based on digital (153, 226, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 113, 225)-net over F₁₆, using
  - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
      - a function field by GarcÃa and Quoos [i]

(220−67, 220, 846)-Net over F₄ — Digital

Digital (153, 220, 846)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−67, 220, 43396)-Net in Base 4 — Upper bound on s

There is no (153, 220, 43397)-net in base 4, because

1 times m-reduction [i] would yield (153, 219, 43397)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 710228 096146 143909 071583 502216 635231 088463 684228 064969 450772 271958 381633 213758 698616 419383 452603 540682 430716 708151 903349 619528 613312 > 4²¹⁹ [i]