MinT - Best Known (240−108, 240, s)-Nets in Base 2

Best Known (240−108, 240, s)-Nets in Base 2

(240−108, 240, 66)-Net over F₂ — Constructive and digital

Digital (132, 240, 66)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (39, 93, 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 (39, 147, 33)-net over F₂, using
  - net from sequence [i] based on digital (39, 32)-sequence over F₂ (see above)

(240−108, 240, 82)-Net over F₂ — Digital

Digital (132, 240, 82)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−108, 240, 296)-Net in Base 2 — Upper bound on s

There is no (132, 240, 297)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2²⁴⁰, 297, S₂, 108), but
- the linear programming bound shows that MÂ â‰¥ 28020 398795 768772 015654 276848 365160 205592 563190 101250 876110 646415 347830 039205 258520 634937 311232 / 15527 302685 925212 739375 > 2²⁴⁰ [i]