MinT - Best Known (167−47, 167, s)-Nets in Base 2

Best Known (167−47, 167, s)-Nets in Base 2

(167−47, 167, 112)-Net over F₂ — Constructive and digital

Digital (120, 167, 112)-net over F₂, using

7 times m-reduction [i] based on digital (120, 174, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 87, 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]

(167−47, 167, 179)-Net over F₂ — Digital

Digital (120, 167, 179)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(167−47, 167, 1369)-Net in Base 2 — Upper bound on s

There is no (120, 167, 1370)-net in base 2, because

1 times m-reduction [i] would yield (120, 166, 1370)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 94 256201 179817 551139 068067 433993 009372 718107 803932 > 2¹⁶⁶ [i]