MinT - Best Known (246−102, 246, s)-Nets in Base 2

Best Known (246−102, 246, s)-Nets in Base 2

(246−102, 246, 75)-Net over F₂ — Constructive and digital

Digital (144, 246, 75)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (39, 90, 33)-net over F₂, using
  - net from sequence [i] based on digital (39, 32)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]
2. digital (54, 156, 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]

(246−102, 246, 101)-Net over F₂ — Digital

Digital (144, 246, 101)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−102, 246, 490)-Net in Base 2 — Upper bound on s

There is no (144, 246, 491)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 117 604905 721961 936858 760821 229396 997976 169698 689688 549627 814211 150969 072072 > 2²⁴⁶ [i]