MinT - Best Known (114−24, 114, s)-Nets in Base 8

Best Known (114−24, 114, s)-Nets in Base 8

(114−24, 114, 2733)-Net over F₈ — Constructive and digital

Digital (90, 114, 2733)-net over F₈, using

8¹ times duplication [i] based on digital (89, 113, 2733)-net over F₈, using
- t-expansion [i] based on digital (88, 113, 2733)-net over F₈, using
  - net defined by OOA [i] based on linear OOA(8¹¹³, 2733, F₈, 25, 25) (dual of [(2733, 25), 68212, 26]-NRT-code), using
    - OOA 12-folding and stacking with additional row [i] based on linear OA(8¹¹³, 32797, F₈, 25) (dual of [32797, 32684, 26]-code), using
      - discarding factors / shortening the dual code based on linear OA(8¹¹³, 32800, F₈, 25) (dual of [32800, 32687, 26]-code), using
        constructionÂ X applied to C_e(24) âŠ‚ C_e(18) [i] based on
        linear OA(8¹⁰⁶, 32768, F₈, 25) (dual of [32768, 32662, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
        linear OA(8⁸¹, 32768, F₈, 19) (dual of [32768, 32687, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
        linear OA(8⁷, 32, F₈, 5) (dual of [32, 25, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(8⁷, 57, F₈, 5) (dual of [57, 50, 6]-code), using
        a code by Danev and Olsson [i]

(114−24, 114, 40333)-Net over F₈ — Digital

Digital (90, 114, 40333)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(114−24, 114, large)-Net in Base 8 — Upper bound on s

There is no (90, 114, large)-net in base 8, because

22 times m-reduction [i] would yield (90, 92, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]