MinT - Best Known (115, 115+47, s)-Nets in Base 2

Best Known (115, 115+47, s)-Nets in Base 2

(115, 115+47, 112)-Net over F₂ — Constructive and digital

Digital (115, 162, 112)-net over F₂, using

2 times m-reduction [i] based on digital (115, 164, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 82, 56)-net over F₄, using
  - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(115, 115+47, 162)-Net over F₂ — Digital

Digital (115, 162, 162)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 115+47, 1173)-Net in Base 2 — Upper bound on s

There is no (115, 162, 1174)-net in base 2, because

1 times m-reduction [i] would yield (115, 161, 1174)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 961335 228821 959829 637522 530423 915012 626523 242348 > 2¹⁶¹ [i]