MinT - Best Known (108, 108+23, s)-Nets in Base 9

Best Known (108, 108+23, s)-Nets in Base 9

(108, 108+23, 48316)-Net over F₉ — Constructive and digital

Digital (108, 131, 48316)-net over F₉, using

9³ times duplication [i] based on digital (105, 128, 48316)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9¹²⁸, 48316, F₉, 23, 23) (dual of [(48316, 23), 1111140, 24]-NRT-code), using
  - OOA 11-folding and stacking with additional row [i] based on linear OA(9¹²⁸, 531477, F₉, 23) (dual of [531477, 531349, 24]-code), using
    - discarding factors / shortening the dual code based on linear OA(9¹²⁸, 531478, F₉, 23) (dual of [531478, 531350, 24]-code), using
      - constructionÂ X applied to C_e(22) âŠ‚ C_e(16) [i] based on
        linear OA(9¹²¹, 531441, F₉, 23) (dual of [531441, 531320, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 9⁶âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
        linear OA(9⁹¹, 531441, F₉, 17) (dual of [531441, 531350, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 9⁶âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
        linear OA(9⁷, 37, F₉, 5) (dual of [37, 30, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(9⁷, 73, F₉, 5) (dual of [73, 66, 6]-code), using
        a code by Danev and Olsson [i]

(108, 108+23, 544317)-Net over F₉ — Digital

Digital (108, 131, 544317)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+23, large)-Net in Base 9 — Upper bound on s

There is no (108, 131, large)-net in base 9, because

21 times m-reduction [i] would yield (108, 110, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]