MinT - Best Known (113, 113+37, s)-Nets in Base 2

Best Known (113, 113+37, s)-Nets in Base 2

(113, 113+37, 144)-Net over F₂ — Constructive and digital

Digital (113, 150, 144)-net over F₂, using

3 times m-reduction [i] based on digital (113, 153, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 51, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(113, 113+37, 229)-Net over F₂ — Digital

Digital (113, 150, 229)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(113, 113+37, 2317)-Net in Base 2 — Upper bound on s

There is no (113, 150, 2318)-net in base 2, because

1 times m-reduction [i] would yield (113, 149, 2318)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 714 680310 099546 930346 157868 215192 699518 876384 > 2¹⁴⁹ [i]