MinT - Best Known (85, 85+15, s)-Nets in Base 3

Best Known (85, 85+15, s)-Nets in Base 3

Digital (85, 100, 8435)-net over F₃, using

net defined by OOA [i] based on linear OOA(3¹⁰⁰, 8435, F₃, 15, 15) (dual of [(8435, 15), 126425, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3¹⁰⁰, 59046, F₃, 15) (dual of [59046, 58946, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁰⁰, 59048, F₃, 15) (dual of [59048, 58948, 16]-code), using
    - 1 times truncation [i] based on linear OA(3¹⁰¹, 59049, F₃, 16) (dual of [59049, 58948, 17]-code), using
      - an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Digital (85, 100, 20825)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹⁰⁰, 20825, F₃, 2, 15) (dual of [(20825, 2), 41550, 16]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹⁰⁰, 29524, F₃, 2, 15) (dual of [(29524, 2), 58948, 16]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁰⁰, 59048, F₃, 15) (dual of [59048, 58948, 16]-code), using
    - 1 times truncation [i] based on linear OA(3¹⁰¹, 59049, F₃, 16) (dual of [59049, 58948, 17]-code), using
      - an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

There is no (85, 100, large)-net in base 3, because

13 times m-reduction [i] would yield (85, 87, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]