MinT - Best Known (217−65, 217, s)-Nets in Base 2

Best Known (217−65, 217, s)-Nets in Base 2

(217−65, 217, 112)-Net over F₂ — Constructive and digital

Digital (152, 217, 112)-net over F₂, using

21 times m-reduction [i] based on digital (152, 238, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 119, 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]

(217−65, 217, 192)-Net over F₂ — Digital

Digital (152, 217, 192)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−65, 217, 1329)-Net in Base 2 — Upper bound on s

There is no (152, 217, 1330)-net in base 2, because

1 times m-reduction [i] would yield (152, 216, 1330)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 105518 618093 064430 072878 977123 152475 252517 947573 259541 356406 407735 > 2²¹⁶ [i]