MinT - Best Known (155−34, 155, s)-Nets in Base 8

Best Known (155−34, 155, s)-Nets in Base 8

(155−34, 155, 1929)-Net over F₈ — Constructive and digital

Digital (121, 155, 1929)-net over F₈, using

8³ times duplication [i] based on digital (118, 152, 1929)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8¹⁵², 1929, F₈, 34, 34) (dual of [(1929, 34), 65434, 35]-NRT-code), using
  - OA 17-folding and stacking [i] based on linear OA(8¹⁵², 32793, F₈, 34) (dual of [32793, 32641, 35]-code), using
    - discarding factors / shortening the dual code based on linear OA(8¹⁵², 32794, F₈, 34) (dual of [32794, 32642, 35]-code), using
      - constructionÂ X applied to C_e(33) âŠ‚ C_e(28) [i] based on
        linear OA(8¹⁴⁶, 32768, F₈, 34) (dual of [32768, 32622, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
        linear OA(8¹²⁶, 32768, F₈, 29) (dual of [32768, 32642, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
        linear OA(8⁶, 26, F₈, 4) (dual of [26, 20, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(8⁶, 56, F₈, 4) (dual of [56, 50, 5]-code), using
        1 times truncation [i] based on linear OA(8⁷, 57, F₈, 5) (dual of [57, 50, 6]-code), using
        a code by Danev and Olsson [i]

(155−34, 155, 32829)-Net over F₈ — Digital

Digital (121, 155, 32829)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(155−34, 155, large)-Net in Base 8 — Upper bound on s

There is no (121, 155, large)-net in base 8, because

32 times m-reduction [i] would yield (121, 123, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]