MinT - Best Known (246−61, 246, s)-Nets in Base 4

Best Known (246−61, 246, s)-Nets in Base 4

(246−61, 246, 1028)-Net over F₄ — Constructive and digital

Digital (185, 246, 1028)-net over F₄, using

4² times duplication [i] based on digital (183, 244, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 61, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(246−61, 246, 2303)-Net over F₄ — Digital

Digital (185, 246, 2303)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−61, 246, 331480)-Net in Base 4 — Upper bound on s

There is no (185, 246, 331481)-net in base 4, because

1 times m-reduction [i] would yield (185, 245, 331481)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3196 683831 310418 937636 448093 920322 130355 165460 460765 279742 694072 895453 797257 557968 215249 707874 382989 633732 972459 171002 443346 199452 649570 137293 097632 > 4²⁴⁵ [i]