MinT - Best Known (256−72, 256, s)-Nets in Base 4

Best Known (256−72, 256, s)-Nets in Base 4

(256−72, 256, 531)-Net over F₄ — Constructive and digital

Digital (184, 256, 531)-net over F₄, using

t-expansion [i] based on digital (179, 256, 531)-net over F₄, using
- 2 times m-reduction [i] based on digital (179, 258, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 86, 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]

(256−72, 256, 1348)-Net over F₄ — Digital

Digital (184, 256, 1348)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−72, 256, 90947)-Net in Base 4 — Upper bound on s

There is no (184, 256, 90948)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13410 758366 513353 640242 260662 305869 015023 550750 836464 211657 563907 815281 693293 429226 846057 456639 632199 327354 153392 105909 114810 126722 953898 094324 112998 280400 > 4²⁵⁶ [i]