MinT - Best Known (145, 145+21, s)-Nets in Base 4

Best Known (145, 145+21, s)-Nets in Base 4

Digital (145, 166, 419430)-net over F₄, using

net defined by OOA [i] based on linear OOA(4¹⁶⁶, 419430, F₄, 21, 21) (dual of [(419430, 21), 8807864, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4¹⁶⁶, 4194301, F₄, 21) (dual of [4194301, 4194135, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁶⁶, 4194304, F₄, 21) (dual of [4194304, 4194138, 22]-code), using
    - an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

Digital (145, 166, 1398101)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(4¹⁶⁶, 1398101, F₄, 3, 21) (dual of [(1398101, 3), 4194137, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4¹⁶⁶, 4194303, F₄, 21) (dual of [4194303, 4194137, 22]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁶⁶, 4194304, F₄, 21) (dual of [4194304, 4194138, 22]-code), using
    - an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

There is no (145, 166, large)-net in base 4, because

19 times m-reduction [i] would yield (145, 147, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]