MinT - Best Known (129, 222, s)-Nets in Base 2

Best Known (129, 222, s)-Nets in Base 2

(129, 222, 66)-Net over F₂ — Constructive and digital

Digital (129, 222, 66)-net over F₂, using

6 times m-reduction [i] based on digital (129, 228, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 114, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(129, 222, 91)-Net over F₂ — Digital

Digital (129, 222, 91)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(129, 222, 438)-Net in Base 2 — Upper bound on s

There is no (129, 222, 439)-net in base 2, because

1 times m-reduction [i] would yield (129, 221, 439)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 569419 174161 464475 563621 566648 158009 573865 246605 532382 392041 570990 > 2²²¹ [i]