MinT - Best Known (154, 154+63, s)-Nets in Base 2

Best Known (154, 154+63, s)-Nets in Base 2

(154, 154+63, 135)-Net over F₂ — Constructive and digital

Digital (154, 217, 135)-net over F₂, using

2¹ times duplication [i] based on digital (153, 216, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 72, 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]

(154, 154+63, 207)-Net over F₂ — Digital

Digital (154, 217, 207)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(154, 154+63, 1508)-Net in Base 2 — Upper bound on s

There is no (154, 217, 1509)-net in base 2, because

1 times m-reduction [i] would yield (154, 216, 1509)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 105514 054714 090063 173580 857875 534586 412232 798083 517607 587280 828960 > 2²¹⁶ [i]