MinT - Best Known (158, 260, s)-Nets in Base 2

Best Known (158, 260, s)-Nets in Base 2

(158, 260, 78)-Net over F₂ — Constructive and digital

Digital (158, 260, 78)-net over F₂, using

2¹ times duplication [i] based on digital (157, 259, 78)-net over F₂, using
- t-expansion [i] based on digital (156, 259, 78)-net over F₂, using
  - (u,Â u+v)-construction [i] based on
    1. digital (51, 102, 36)-net over F₂, using
      - net from sequence [i] based on digital (51, 35)-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 3 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, 157, 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]

(158, 260, 84)-Net in Base 2 — Constructive

(158, 260, 84)-net in base 2, using

t-expansion [i] based on (157, 260, 84)-net in base 2, using
- trace code for nets [i] based on (27, 130, 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]

(158, 260, 121)-Net over F₂ — Digital

Digital (158, 260, 121)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(158, 260, 607)-Net in Base 2 — Upper bound on s

There is no (158, 260, 608)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 897672 801215 722155 361402 713507 633928 813151 098587 820316 624418 880361 655624 753374 > 2²⁶⁰ [i]