MinT - Best Known (210−21, 210, s)-Nets in Base 3

Best Known (210−21, 210, s)-Nets in Base 3

Digital (189, 210, 838860)-net over F₃, using

net defined by OOA [i] based on linear OOA(3²¹⁰, 838860, F₃, 21, 21) (dual of [(838860, 21), 17615850, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3²¹⁰, 8388601, F₃, 21) (dual of [8388601, 8388391, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²¹⁰, large, F₃, 21) (dual of [large, large−210, 22]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

Digital (189, 210, 2315075)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3²¹⁰, 2315075, F₃, 3, 21) (dual of [(2315075, 3), 6945015, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3²¹⁰, 2796201, F₃, 3, 21) (dual of [(2796201, 3), 8388393, 22]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3²¹⁰, large, F₃, 21) (dual of [large, large−210, 22]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]

There is no (189, 210, large)-net in base 3, because

19 times m-reduction [i] would yield (189, 191, large)-net in base 3, but
- mutually orthogonal hypercube bound [i]