MinT - Best Known (238−77, 238, s)-Nets in Base 4

Best Known (238−77, 238, s)-Nets in Base 4

(238−77, 238, 450)-Net over F₄ — Constructive and digital

Digital (161, 238, 450)-net over F₄, using

4 times m-reduction [i] based on digital (161, 242, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 121, 225)-net over F₁₆, using
  - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
      - a function field by GarcÃa and Quoos [i]

(238−77, 238, 716)-Net over F₄ — Digital

Digital (161, 238, 716)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−77, 238, 28455)-Net in Base 4 — Upper bound on s

There is no (161, 238, 28456)-net in base 4, because

1 times m-reduction [i] would yield (161, 237, 28456)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48837 270450 167774 816183 449913 166397 920300 486181 400711 944931 005173 189052 797953 367310 384994 897933 395815 217987 513716 441167 619178 594262 514770 948575 > 4²³⁷ [i]