MinT - Best Known (237−71, 237, s)-Nets in Base 2

Best Known (237−71, 237, s)-Nets in Base 2

(237−71, 237, 112)-Net over F₂ — Constructive and digital

Digital (166, 237, 112)-net over F₂, using

t-expansion [i] based on digital (163, 237, 112)-net over F₂, using
- 23 times m-reduction [i] based on digital (163, 260, 112)-net over F₂, using
  - trace code for nets [i] based on digital (33, 130, 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]

(237−71, 237, 207)-Net over F₂ — Digital

Digital (166, 237, 207)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−71, 237, 1438)-Net in Base 2 — Upper bound on s

There is no (166, 237, 1439)-net in base 2, because

1 times m-reduction [i] would yield (166, 236, 1439)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 111986 777806 802262 067964 945299 374151 799894 586501 349797 190469 002884 498152 > 2²³⁶ [i]