MinT - Best Known (115−42, 115, s)-Nets in Base 2

Best Known (115−42, 115, s)-Nets in Base 2

(115−42, 115, 66)-Net over F₂ — Constructive and digital

Digital (73, 115, 66)-net over F₂, using

1 times m-reduction [i] based on digital (73, 116, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 58, 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]

(115−42, 115, 73)-Net over F₂ — Digital

Digital (73, 115, 73)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(115−42, 115, 356)-Net in Base 2 — Upper bound on s

There is no (73, 115, 357)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 42817 443494 303979 353805 108646 812804 > 2¹¹⁵ [i]