MinT - Best Known (144, 226, s)-Nets in Base 2

Best Known (144, 226, s)-Nets in Base 2

(144, 226, 77)-Net over F₂ — Constructive and digital

Digital (144, 226, 77)-net over F₂, using

2 times m-reduction [i] based on digital (144, 228, 77)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (48, 90, 35)-net over F₂, using
    - net from sequence [i] based on digital (48, 34)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 41, N(F)Â =Â 32, 1 place with degree 2, and 2 places with degree 4 [i] based on function field F/F₂ with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
  2. digital (54, 138, 42)-net over F₂, using
    - net from sequence [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]

(144, 226, 86)-Net in Base 2 — Constructive

(144, 226, 86)-net in base 2, using

2 times m-reduction [i] based on (144, 228, 86)-net in base 2, using
- trace code for nets [i] based on (30, 114, 43)-net in base 4, using
  - net from sequence [i] based on (30, 42)-sequence in base 4, using
    - base expansion [i] based on digital (60, 42)-sequence over F₂, using
      - t-expansion [i] based on digital (59, 42)-sequence over F₂, using
        Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 54, N(F)Â =Â 42, and 1 place with degree 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]

(144, 226, 128)-Net over F₂ — Digital

Digital (144, 226, 128)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 226, 677)-Net in Base 2 — Upper bound on s

There is no (144, 226, 678)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 108 795624 387455 659630 511610 432112 003825 217331 079943 452102 093302 964368 > 2²²⁶ [i]