MinT - Best Known (147−35, 147, s)-Nets in Base 2

Best Known (147−35, 147, s)-Nets in Base 2

Digital (112, 147, 195)-net over F₂, using

trace code for nets [i] based on digital (14, 49, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

Digital (112, 147, 253)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2¹⁴⁷, 253, F₂, 2, 35) (dual of [(253, 2), 359, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁴⁷, 257, F₂, 2, 35) (dual of [(257, 2), 367, 36]-NRT-code), using
  - 1 times NRT-code embedding in larger space [i] based on linear OOA(2¹⁴⁵, 256, F₂, 2, 35) (dual of [(256, 2), 367, 36]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2¹⁴⁵, 512, F₂, 35) (dual of [512, 367, 36]-code), using
      - an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 511Â = 2⁹âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]

There is no (112, 147, 2738)-net in base 2, because

1 times m-reduction [i] would yield (112, 146, 2738)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 89 563956 995163 781303 093725 927129 443178 849429 > 2¹⁴⁶ [i]