MinT - Best Known (228−99, 228, s)-Nets in Base 2

Best Known (228−99, 228, s)-Nets in Base 2

(228−99, 228, 66)-Net over F₂ — Constructive and digital

Digital (129, 228, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 114, 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]

(228−99, 228, 86)-Net over F₂ — Digital

Digital (129, 228, 86)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−99, 228, 405)-Net in Base 2 — Upper bound on s

There is no (129, 228, 406)-net in base 2, because

1 times m-reduction [i] would yield (129, 227, 406)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 219 028452 841642 845539 033985 422006 833140 634252 289690 183519 734200 539684 > 2²²⁷ [i]