MinT - Best Known (128, 178, s)-Nets in Base 2

Best Known (128, 178, s)-Nets in Base 2

(128, 178, 135)-Net over F₂ — Constructive and digital

Digital (128, 178, 135)-net over F₂, using

2¹ times duplication [i] based on digital (127, 177, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 59, 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]

(128, 178, 189)-Net over F₂ — Digital

Digital (128, 178, 189)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 178, 1379)-Net in Base 2 — Upper bound on s

There is no (128, 178, 1380)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 389282 955588 887594 767788 661335 174198 024799 782066 170212 > 2¹⁷⁸ [i]