MinT - Best Known (89, 100, s)-Nets in Base 4

Best Known (89, 100, s)-Nets in Base 4

Digital (89, 100, 1677720)-net over F₄, using

4³ times duplication [i] based on digital (86, 97, 1677720)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4⁹⁷, 1677720, F₄, 11, 11) (dual of [(1677720, 11), 18454823, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(4⁹⁷, 8388601, F₄, 11) (dual of [8388601, 8388504, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(4⁹⁷, large, F₄, 11) (dual of [large, large−97, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

Digital (89, 100, 5798152)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4¹⁰⁰, 5798152, F₄, 11) (dual of [5798152, 5798052, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(4¹⁰⁰, large, F₄, 11) (dual of [large, large−100, 12]-code), using
  - 3 times code embedding in larger space [i] based on linear OA(4⁹⁷, large, F₄, 11) (dual of [large, large−97, 12]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]

There is no (89, 100, large)-net in base 4, because