MinT - Best Known (150, 258, s)-Nets in Base 4

Best Known (150, 258, s)-Nets in Base 4

(150, 258, 138)-Net over F₄ — Constructive and digital

Digital (150, 258, 138)-net over F₄, using

t-expansion [i] based on digital (149, 258, 138)-net over F₄, using
- 1 times m-reduction [i] based on digital (149, 259, 138)-net over F₄, using
  - (u,Â u+v)-construction [i] based on
    1. digital (21, 76, 34)-net over F₄, using
      - net from sequence [i] based on digital (21, 33)-sequence over F₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
        T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
    2. digital (73, 183, 104)-net over F₄, using
      - net from sequence [i] based on digital (73, 103)-sequence over F₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
        F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(150, 258, 317)-Net over F₄ — Digital

Digital (150, 258, 317)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 258, 5214)-Net in Base 4 — Upper bound on s

There is no (150, 258, 5215)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 214581 011470 848447 133068 149937 060551 898151 510409 788556 410405 672475 983326 646426 648562 697769 656243 576252 194420 526099 695573 434117 936803 888463 193221 527800 795170 > 4²⁵⁸ [i]