MinT - Best Known (246−106, 246, s)-Nets in Base 4

Best Known (246−106, 246, s)-Nets in Base 4

(246−106, 246, 134)-Net over F₄ — Constructive and digital

Digital (140, 246, 134)-net over F₄, using

2 times m-reduction [i] based on digital (140, 248, 134)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (13, 67, 30)-net over F₄, using
    - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
        F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
  2. digital (73, 181, 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]

(246−106, 246, 276)-Net over F₄ — Digital

Digital (140, 246, 276)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−106, 246, 4233)-Net in Base 4 — Upper bound on s

There is no (140, 246, 4234)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12869 375262 129121 986244 107052 434214 037265 482167 330593 318853 334204 259463 516260 054182 779159 066787 076495 245754 836057 879031 005785 698106 878064 522283 717392 > 4²⁴⁶ [i]