MinT - Best Known (96, 96+11, s)-Nets in Base 3

Best Known (96, 96+11, s)-Nets in Base 3

(96, 96+11, 1677720)-Net over F₃ — Constructive and digital

Digital (96, 107, 1677720)-net over F₃, using

3¹ times duplication [i] based on 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]

(96, 96+11, 3442514)-Net over F₃ — Digital

Digital (96, 107, 3442514)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹⁰⁷, 3442514, F₃, 2, 11) (dual of [(3442514, 2), 6884921, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹⁰⁷, 4194301, F₃, 2, 11) (dual of [(4194301, 2), 8388495, 12]-NRT-code), using
  - 3¹ times duplication [i] 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]

(96, 96+11, large)-Net in Base 3 — Upper bound on s

There is no (96, 107, large)-net in base 3, because

9 times m-reduction [i] would yield (96, 98, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]