Best Known (55, 55+28, s)-Nets in Base 64
(55, 55+28, 18725)-Net over F64 — Constructive and digital
Digital (55, 83, 18725)-net over F64, using
- net defined by OOA [i] based on linear OOA(6483, 18725, F64, 28, 28) (dual of [(18725, 28), 524217, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(6483, 262150, F64, 28) (dual of [262150, 262067, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(6483, 262151, F64, 28) (dual of [262151, 262068, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(6482, 262144, F64, 28) (dual of [262144, 262062, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(6476, 262144, F64, 26) (dual of [262144, 262068, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(6483, 262151, F64, 28) (dual of [262151, 262068, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(6483, 262150, F64, 28) (dual of [262150, 262067, 29]-code), using
(55, 55+28, 114885)-Net over F64 — Digital
Digital (55, 83, 114885)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6483, 114885, F64, 2, 28) (dual of [(114885, 2), 229687, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6483, 131075, F64, 2, 28) (dual of [(131075, 2), 262067, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6483, 262150, F64, 28) (dual of [262150, 262067, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(6483, 262151, F64, 28) (dual of [262151, 262068, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(6482, 262144, F64, 28) (dual of [262144, 262062, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(6476, 262144, F64, 26) (dual of [262144, 262068, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(6483, 262151, F64, 28) (dual of [262151, 262068, 29]-code), using
- OOA 2-folding [i] based on linear OA(6483, 262150, F64, 28) (dual of [262150, 262067, 29]-code), using
- discarding factors / shortening the dual code based on linear OOA(6483, 131075, F64, 2, 28) (dual of [(131075, 2), 262067, 29]-NRT-code), using
(55, 55+28, large)-Net in Base 64 — Upper bound on s
There is no (55, 83, large)-net in base 64, because
- 26 times m-reduction [i] would yield (55, 57, large)-net in base 64, but