MinT - Best Known (167−48, 167, s)-Nets in Base 2

Best Known (167−48, 167, s)-Nets in Base 2

(167−48, 167, 112)-Net over F₂ — Constructive and digital

Digital (119, 167, 112)-net over F₂, using

5 times m-reduction [i] based on digital (119, 172, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 86, 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]

(167−48, 167, 170)-Net over F₂ — Digital

Digital (119, 167, 170)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(167−48, 167, 1184)-Net in Base 2 — Upper bound on s

There is no (119, 167, 1185)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 190 649877 000249 891560 509814 007919 616921 031782 786348 > 2¹⁶⁷ [i]