MinT - Best Known (128, 128+53, s)-Nets in Base 4

Best Known (128, 128+53, s)-Nets in Base 4

(128, 128+53, 531)-Net over F₄ — Constructive and digital

Digital (128, 181, 531)-net over F₄, using

4¹ times duplication [i] based on digital (127, 180, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 60, 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]

(128, 128+53, 846)-Net over F₄ — Digital

Digital (128, 181, 846)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 128+53, 51772)-Net in Base 4 — Upper bound on s

There is no (128, 181, 51773)-net in base 4, because

1 times m-reduction [i] would yield (128, 180, 51773)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 348740 132278 427602 900787 718255 759872 056328 540114 238314 586630 983822 448616 005470 823366 645680 278114 602190 060430 > 4¹⁸⁰ [i]