MinT - Best Known (161, 161+60, s)-Nets in Base 4

Best Known (161, 161+60, s)-Nets in Base 4

(161, 161+60, 531)-Net over F₄ — Constructive and digital

Digital (161, 221, 531)-net over F₄, using

10 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+60, 1395)-Net over F₄ — Digital

Digital (161, 221, 1395)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(161, 161+60, 109331)-Net in Base 4 — Upper bound on s

There is no (161, 221, 109332)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 358353 359046 082122 780889 704101 344262 417715 320277 144709 466186 565281 463084 379279 145790 523072 081930 241081 221764 172599 124728 178089 851456 > 4²²¹ [i]