MinT - Best Known (236−85, 236, s)-Nets in Base 2

Best Known (236−85, 236, s)-Nets in Base 2

(236−85, 236, 112)-Net over F₂ — Constructive and digital

Digital (151, 236, 112)-net over F₂, using

trace code for nets [i] based on digital (33, 118, 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]

(236−85, 236, 135)-Net over F₂ — Digital

Digital (151, 236, 135)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−85, 236, 737)-Net in Base 2 — Upper bound on s

There is no (151, 236, 738)-net in base 2, because

1 times m-reduction [i] would yield (151, 235, 738)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 55522 418292 314953 948910 137606 025902 106554 197839 079164 821246 465124 338144 > 2²³⁵ [i]