Best Known (21, 21+4, s)-Nets in Base 32
(21, 21+4, large)-Net over F32 — Constructive and digital
Digital (21, 25, large)-net over F32, using
- t-expansion [i] based on digital (20, 25, large)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 0, 524289)-net over F32, using
- s-reduction based on digital (0, 0, s)-net over F32 with arbitrarily large s, using
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 0, 524289)-net over F32 (see above)
- digital (0, 1, 524289)-net over F32, using
- s-reduction based on digital (0, 1, s)-net over F32 with arbitrarily large s, using
- digital (0, 1, 524289)-net over F32 (see above)
- digital (0, 1, 524289)-net over F32 (see above)
- digital (3, 5, 524289)-net over F32, using
- s-reduction based on digital (3, 5, 1082401)-net over F32, using
- digital (12, 17, 524289)-net over F32, using
- net defined by OOA [i] based on linear OOA(3217, 524289, F32, 5, 5) (dual of [(524289, 5), 2621428, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(3217, 1048579, F32, 5) (dual of [1048579, 1048562, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(3217, 1048580, F32, 5) (dual of [1048580, 1048563, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(3217, 1048576, F32, 5) (dual of [1048576, 1048559, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(3213, 1048576, F32, 4) (dual of [1048576, 1048563, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(3217, 1048580, F32, 5) (dual of [1048580, 1048563, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(3217, 1048579, F32, 5) (dual of [1048579, 1048562, 6]-code), using
- net defined by OOA [i] based on linear OOA(3217, 524289, F32, 5, 5) (dual of [(524289, 5), 2621428, 6]-NRT-code), using
- digital (0, 0, 524289)-net over F32, using
- generalized (u, u+v)-construction [i] based on
(21, 21+4, large)-Net in Base 32 — Upper bound on s
There is no (21, 25, large)-net in base 32, because
- 2 times m-reduction [i] would yield (21, 23, large)-net in base 32, but