MinT - Best Known (143, 143+103, s)-Nets in Base 2

Best Known (143, 143+103, s)-Nets in Base 2

(143, 143+103, 70)-Net over F₂ — Constructive and digital

Digital (143, 246, 70)-net over F₂, using

1 times m-reduction [i] based on digital (143, 247, 70)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (21, 73, 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 (70, 174, 49)-net over F₂, using
    - net from sequence [i] based on digital (70, 48)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 69, N(F)Â =Â 48, and 1 place with degree 2 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]

(143, 143+103, 99)-Net over F₂ — Digital

Digital (143, 246, 99)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(143, 143+103, 483)-Net in Base 2 — Upper bound on s

There is no (143, 246, 484)-net in base 2, because

1 times m-reduction [i] would yield (143, 245, 484)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 61 811109 432061 650805 051343 546437 102541 518554 885151 551874 322262 155528 633260 > 2²⁴⁵ [i]