MinT - Best Known (202−58, 202, s)-Nets in Base 2

Best Known (202−58, 202, s)-Nets in Base 2

(202−58, 202, 135)-Net over F₂ — Constructive and digital

Digital (144, 202, 135)-net over F₂, using

2¹ times duplication [i] based on digital (143, 201, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 67, 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]

(202−58, 202, 200)-Net over F₂ — Digital

Digital (144, 202, 200)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−58, 202, 1416)-Net in Base 2 — Upper bound on s

There is no (144, 202, 1417)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 527890 152672 805968 025077 500634 981833 306135 379325 599387 117504 > 2²⁰² [i]