MinT - Best Known (208−60, 208, s)-Nets in Base 2

Best Known (208−60, 208, s)-Nets in Base 2

(208−60, 208, 135)-Net over F₂ — Constructive and digital

Digital (148, 208, 135)-net over F₂, using

2¹ times duplication [i] based on digital (147, 207, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 69, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(208−60, 208, 203)-Net over F₂ — Digital

Digital (148, 208, 203)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−60, 208, 1428)-Net in Base 2 — Upper bound on s

There is no (148, 208, 1429)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 418 303723 837804 882360 484536 909557 092876 154436 314632 468242 988928 > 2²⁰⁸ [i]