MinT - Best Known (202−72, 202, s)-Nets in Base 2

Best Known (202−72, 202, s)-Nets in Base 2

(202−72, 202, 75)-Net over F₂ — Constructive and digital

Digital (130, 202, 75)-net over F₂, using

2 times m-reduction [i] based on digital (130, 204, 75)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 76, 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, 128, 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]

(202−72, 202, 84)-Net in Base 2 — Constructive

(130, 202, 84)-net in base 2, using

4 times m-reduction [i] based on (130, 206, 84)-net in base 2, using
- trace code for nets [i] based on (27, 103, 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]

(202−72, 202, 121)-Net over F₂ — Digital

Digital (130, 202, 121)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−72, 202, 646)-Net in Base 2 — Upper bound on s

There is no (130, 202, 647)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 667329 990363 382153 194859 091614 264795 324276 347304 612647 442996 > 2²⁰² [i]