MinT - Best Known (106−11, 106, s)-Nets in Base 3

Best Known (106−11, 106, s)-Nets in Base 3

Digital (95, 106, 1677720)-net over F₃, using

net defined by OOA [i] based on linear OOA(3¹⁰⁶, 1677720, F₃, 11, 11) (dual of [(1677720, 11), 18454814, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(3¹⁰⁶, 8388601, F₃, 11) (dual of [8388601, 8388495, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁰⁶, large, F₃, 11) (dual of [large, large−106, 12]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]

Digital (95, 106, 3000788)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹⁰⁶, 3000788, F₃, 2, 11) (dual of [(3000788, 2), 6001470, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹⁰⁶, 4194301, F₃, 2, 11) (dual of [(4194301, 2), 8388496, 12]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁰⁶, 8388602, F₃, 11) (dual of [8388602, 8388496, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁰⁶, large, F₃, 11) (dual of [large, large−106, 12]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]

There is no (95, 106, large)-net in base 3, because