MinT - Best Known (154, 260, s)-Nets in Base 4

Best Known (154, 260, s)-Nets in Base 4

(154, 260, 138)-Net over F₄ — Constructive and digital

Digital (154, 260, 138)-net over F₄, using

t-expansion [i] based on digital (149, 260, 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, 184, 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]

(154, 260, 146)-Net in Base 4 — Constructive

(154, 260, 146)-net in base 4, using

t-expansion [i] based on (153, 260, 146)-net in base 4, using
- (u,Â u+v)-construction [i] based on
  1. (27, 80, 42)-net in base 4, using
    - net from sequence [i] based on (27, 41)-sequence in base 4, using
      - base expansion [i] based on digital (54, 41)-sequence over F₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
        an explicitly constructive algebraic function field [i]
  2. digital (73, 180, 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]

(154, 260, 347)-Net over F₄ — Digital

Digital (154, 260, 347)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(154, 260, 6124)-Net in Base 4 — Upper bound on s

There is no (154, 260, 6125)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 437175 804035 514979 602379 270676 010412 804709 440395 357618 788160 364012 887141 250660 124222 605201 447192 846956 943668 423530 258276 483282 457639 246847 318061 911130 269936 > 4²⁶⁰ [i]