MinT - Best Known (161, 161+68, s)-Nets in Base 4

Best Known (161, 161+68, s)-Nets in Base 4

(161, 161+68, 531)-Net over F₄ — Constructive and digital

Digital (161, 229, 531)-net over F₄, using

2 times m-reduction [i] based on digital (161, 231, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 77, 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]

(161, 161+68, 971)-Net over F₄ — Digital

Digital (161, 229, 971)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(161, 161+68, 51188)-Net in Base 4 — Upper bound on s

There is no (161, 229, 51189)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 744713 057982 605922 865481 903353 103967 451857 716398 023397 838081 537153 083374 152138 271130 244915 060298 728045 434926 489369 722191 040401 317095 128870 > 4²²⁹ [i]