MinT - Best Known (153, 153+63, s)-Nets in Base 2

Best Known (153, 153+63, s)-Nets in Base 2

(153, 153+63, 135)-Net over F₂ — Constructive and digital

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]

(153, 153+63, 204)-Net over F₂ — Digital

Digital (153, 216, 204)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(153, 153+63, 1474)-Net in Base 2 — Upper bound on s

There is no (153, 216, 1475)-net in base 2, because

1 times m-reduction [i] would yield (153, 215, 1475)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 53141 729250 729265 350429 269986 945172 140078 003258 268065 987797 540000 > 2²¹⁵ [i]