MinT - Best Known (63−28, 63, s)-Nets in Base 2

Best Known (63−28, 63, s)-Nets in Base 2

(63−28, 63, 28)-Net over F₂ — Constructive and digital

Digital (35, 63, 28)-net over F₂, using

1 times m-reduction [i] based on digital (35, 64, 28)-net over F₂, using
- trace code for nets [i] based on digital (3, 32, 14)-net over F₄, using
  - net from sequence [i] based on digital (3, 13)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
      - an explicitly constructive algebraic function field [i]

(63−28, 63, 30)-Net over F₂ — Digital

Digital (35, 63, 30)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(63−28, 63, 116)-Net in Base 2 — Upper bound on s

There is no (35, 63, 117)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2⁶³, 117, S₂, 28), but
- the linear programming bound shows that MÂ â‰¥ 16946 634974 952621 699046 667146 230655 213597 884416 / 1729 294234 965439 779438 380995 > 2⁶³ [i]