MinT - Best Known (242−82, 242, s)-Nets in Base 2

Best Known (242−82, 242, s)-Nets in Base 2

(242−82, 242, 112)-Net over F₂ — Constructive and digital

Digital (160, 242, 112)-net over F₂, using

12 times m-reduction [i] based on digital (160, 254, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 127, 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]

(242−82, 242, 158)-Net over F₂ — Digital

Digital (160, 242, 158)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−82, 242, 906)-Net in Base 2 — Upper bound on s

There is no (160, 242, 907)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7 329343 552008 478318 006161 415876 132688 184975 802698 621156 714651 746228 384400 > 2²⁴² [i]