MinT - Best Known (156, 253, s)-Nets in Base 2

Best Known (156, 253, s)-Nets in Base 2

(156, 253, 84)-Net over F₂ — Constructive and digital

Digital (156, 253, 84)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (54, 102, 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]
2. digital (54, 151, 42)-net over F₂, using
  - net from sequence [i] based on digital (54, 41)-sequence over F₂ (see above)

(156, 253, 124)-Net over F₂ — Digital

Digital (156, 253, 124)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(156, 253, 644)-Net in Base 2 — Upper bound on s

There is no (156, 253, 645)-net in base 2, because

1 times m-reduction [i] would yield (156, 252, 645)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7340 670655 994076 532855 090107 960307 409930 673431 410835 046804 503646 911439 675144 > 2²⁵² [i]