MinT - Best Known (230−82, 230, s)-Nets in Base 2

Best Known (230−82, 230, s)-Nets in Base 2

(230−82, 230, 112)-Net over F₂ — Constructive and digital

Digital (148, 230, 112)-net over F₂, using

trace code for nets [i] based on digital (33, 115, 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]

(230−82, 230, 135)-Net over F₂ — Digital

Digital (148, 230, 135)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−82, 230, 729)-Net in Base 2 — Upper bound on s

There is no (148, 230, 730)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1795 142192 191965 408153 370848 504952 381252 628682 271849 434939 126226 753958 > 2²³⁰ [i]