MinT - Best Known (97, 97+30, s)-Nets in Base 2

Best Known (97, 97+30, s)-Nets in Base 2

(97, 97+30, 144)-Net over F₂ — Constructive and digital

Digital (97, 127, 144)-net over F₂, using

2 times m-reduction [i] based on digital (97, 129, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 43, 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]

(97, 97+30, 225)-Net over F₂ — Digital

Digital (97, 127, 225)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(97, 97+30, 2250)-Net in Base 2 — Upper bound on s

There is no (97, 127, 2251)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 170 693448 843490 129716 119796 511981 939968 > 2¹²⁷ [i]