MinT - Best Known (242−73, 242, s)-Nets in Base 2

Best Known (242−73, 242, s)-Nets in Base 2

(242−73, 242, 112)-Net over F₂ — Constructive and digital

Digital (169, 242, 112)-net over F₂, using

t-expansion [i] based on digital (163, 242, 112)-net over F₂, using
- 18 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]

(242−73, 242, 207)-Net over F₂ — Digital

Digital (169, 242, 207)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−73, 242, 1426)-Net in Base 2 — Upper bound on s

There is no (169, 242, 1427)-net in base 2, because

1 times m-reduction [i] would yield (169, 241, 1427)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 589106 855491 066861 065363 986262 394597 736084 929020 682706 844447 920132 682288 > 2²⁴¹ [i]