MinT - Best Known (148, 148+75, s)-Nets in Base 2

Best Known (148, 148+75, s)-Nets in Base 2

(148, 148+75, 112)-Net over F₂ — Constructive and digital

Digital (148, 223, 112)-net over F₂, using

7 times m-reduction [i] based on digital (148, 230, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 115, 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]

(148, 148+75, 150)-Net over F₂ — Digital

Digital (148, 223, 150)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(148, 148+75, 884)-Net in Base 2 — Upper bound on s

There is no (148, 223, 885)-net in base 2, because

1 times m-reduction [i] would yield (148, 222, 885)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 958742 334277 575674 317031 391313 726162 156195 345783 808922 377228 322706 > 2²²² [i]