MinT - Best Known (88−10, 88, s)-Nets in Base 4

Best Known (88−10, 88, s)-Nets in Base 4

Digital (78, 88, 1677720)-net over F₄, using

4³ times duplication [i] based on digital (75, 85, 1677720)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4⁸⁵, 1677720, F₄, 10, 10) (dual of [(1677720, 10), 16777115, 11]-NRT-code), using
  - OA 5-folding and stacking [i] based on linear OA(4⁸⁵, 8388600, F₄, 10) (dual of [8388600, 8388515, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(4⁸⁵, large, F₄, 10) (dual of [large, large−85, 11]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Digital (78, 88, 4425585)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4⁸⁸, 4425585, F₄, 10) (dual of [4425585, 4425497, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(4⁸⁸, large, F₄, 10) (dual of [large, large−88, 11]-code), using
  - 3 times code embedding in larger space [i] based on linear OA(4⁸⁵, large, F₄, 10) (dual of [large, large−85, 11]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

There is no (78, 88, large)-net in base 4, because