MinT - Best Known (194−83, 194, s)-Nets in Base 2

Best Known (194−83, 194, s)-Nets in Base 2

(194−83, 194, 60)-Net over F₂ — Constructive and digital

Digital (111, 194, 60)-net over F₂, using

2 times m-reduction [i] based on digital (111, 196, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 98, 30)-net over F₄, using
  - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
      - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(194−83, 194, 77)-Net over F₂ — Digital

Digital (111, 194, 77)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−83, 194, 364)-Net in Base 2 — Upper bound on s

There is no (111, 194, 365)-net in base 2, because

1 times m-reduction [i] would yield (111, 193, 365)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13320 278585 242369 671737 691175 209503 313342 942986 519426 813478 > 2¹⁹³ [i]