MinT - Best Known (103−37, 103, s)-Nets in Base 2

Best Known (103−37, 103, s)-Nets in Base 2

(103−37, 103, 60)-Net over F₂ — Constructive and digital

Digital (66, 103, 60)-net over F₂, using

3 times m-reduction [i] based on digital (66, 106, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 53, 30)-net over F₄, using
  - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
      - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(103−37, 103, 69)-Net over F₂ — Digital

Digital (66, 103, 69)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(103−37, 103, 357)-Net in Base 2 — Upper bound on s

There is no (66, 103, 358)-net in base 2, because

1 times m-reduction [i] would yield (66, 102, 358)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 075555 852477 127916 947945 630340 > 2¹⁰² [i]