MinT - Best Known (229−99, 229, s)-Nets in Base 2

Best Known (229−99, 229, s)-Nets in Base 2

(229−99, 229, 66)-Net over F₂ — Constructive and digital

Digital (130, 229, 66)-net over F₂, using

1 times m-reduction [i] based on digital (130, 230, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 115, 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]

(229−99, 229, 87)-Net over F₂ — Digital

Digital (130, 229, 87)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−99, 229, 412)-Net in Base 2 — Upper bound on s

There is no (130, 229, 413)-net in base 2, because

1 times m-reduction [i] would yield (130, 228, 413)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 452 007208 418628 092333 488123 854589 135344 021803 897974 579471 801364 406168 > 2²²⁸ [i]