MinT - Best Known (155, 155+60, s)-Nets in Base 4

Best Known (155, 155+60, s)-Nets in Base 4

(155, 155+60, 531)-Net over F₄ — Constructive and digital

Digital (155, 215, 531)-net over F₄, using

7 times m-reduction [i] based on digital (155, 222, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 74, 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]

(155, 155+60, 1203)-Net over F₄ — Digital

Digital (155, 215, 1203)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(155, 155+60, 82851)-Net in Base 4 — Upper bound on s

There is no (155, 215, 82852)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2772 804085 099808 003138 228628 554552 238837 865954 462584 580624 505617 273925 423114 857579 416459 803223 093308 793467 121760 440722 025310 468984 > 4²¹⁵ [i]