MinT - Best Known (238−104, 238, s)-Nets in Base 2

Best Known (238−104, 238, s)-Nets in Base 2

(238−104, 238, 66)-Net over F₂ — Constructive and digital

Digital (134, 238, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 119, 33)-net over F₄, using
- net from sequence [i] based on digital (15, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(238−104, 238, 87)-Net over F₂ — Digital

Digital (134, 238, 87)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−104, 238, 410)-Net in Base 2 — Upper bound on s

There is no (134, 238, 411)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 468966 333661 303775 231232 729797 714441 852235 168306 986007 544181 810076 542632 > 2²³⁸ [i]