MinT - Best Known (260−122, 260, s)-Nets in Base 2

Best Known (260−122, 260, s)-Nets in Base 2

(260−122, 260, 63)-Net over F₂ — Constructive and digital

Digital (138, 260, 63)-net over F₂, using

2¹ times duplication [i] based on digital (137, 259, 63)-net over F₂, using
- t-expansion [i] based on digital (136, 259, 63)-net over F₂, using
  - (u,Â u+v)-construction [i] based on
    1. digital (21, 82, 21)-net over F₂, using
      - net from sequence [i] based on digital (21, 20)-sequence over F₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 21 and N(F) ≥ 21, using
        an explicitly constructive algebraic function field [i]
    2. digital (54, 177, 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]

(260−122, 260, 81)-Net over F₂ — Digital

Digital (138, 260, 81)-net over F₂, using

t-expansion [i] based on digital (126, 260, 81)-net over F₂, using
- net from sequence [i] based on digital (126, 80)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 126 and N(F) ≥ 81, using
    - Drinfeld modules of rank 1 [i]

(260−122, 260, 368)-Net in Base 2 — Upper bound on s

There is no (138, 260, 369)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 923350 367325 649723 354067 343626 333165 470885 034358 976876 708308 924058 750191 925600 > 2²⁶⁰ [i]