MinT - Best Known (115−73, 115, s)-Nets in Base 2

Best Known (115−73, 115, s)-Nets in Base 2

(115−73, 115, 33)-Net over F₂ — Constructive and digital

Digital (42, 115, 33)-net over F₂, using

t-expansion [i] based on digital (39, 115, 33)-net over F₂, using
- net from sequence [i] based on digital (39, 32)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(115−73, 115, 83)-Net in Base 2 — Upper bound on s

There is no (42, 115, 84)-net in base 2, because

1 times m-reduction [i] would yield (42, 114, 84)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 26999 088582 485279 271597 738396 976600 > 2¹¹⁴ [i]