MinT - Best Known (217−64, 217, s)-Nets in Base 4

Best Known (217−64, 217, s)-Nets in Base 4

(217−64, 217, 531)-Net over F₄ — Constructive and digital

Digital (153, 217, 531)-net over F₄, using

2 times m-reduction [i] based on digital (153, 219, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 73, 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]

(217−64, 217, 954)-Net over F₄ — Digital

Digital (153, 217, 954)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−64, 217, 51553)-Net in Base 4 — Upper bound on s

There is no (153, 217, 51554)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 44376 673633 471449 036171 522774 121158 032429 662625 447550 200692 474536 717468 629356 250232 011632 024605 695115 475898 860308 478202 937294 646375 > 4²¹⁷ [i]