Best Known (22, 30, s)-Nets in Base 16
(22, 30, 32769)-Net over F16 — Constructive and digital
Digital (22, 30, 32769)-net over F16, using
- net defined by OOA [i] based on linear OOA(1630, 32769, F16, 8, 8) (dual of [(32769, 8), 262122, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(1630, 131076, F16, 8) (dual of [131076, 131046, 9]-code), using
- trace code [i] based on linear OA(25615, 65538, F256, 8) (dual of [65538, 65523, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(25613, 65536, F256, 7) (dual of [65536, 65523, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- trace code [i] based on linear OA(25615, 65538, F256, 8) (dual of [65538, 65523, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(1630, 131076, F16, 8) (dual of [131076, 131046, 9]-code), using
(22, 30, 131076)-Net over F16 — Digital
Digital (22, 30, 131076)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1630, 131076, F16, 8) (dual of [131076, 131046, 9]-code), using
- trace code [i] based on linear OA(25615, 65538, F256, 8) (dual of [65538, 65523, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(25613, 65536, F256, 7) (dual of [65536, 65523, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- trace code [i] based on linear OA(25615, 65538, F256, 8) (dual of [65538, 65523, 9]-code), using
(22, 30, large)-Net in Base 16 — Upper bound on s
There is no (22, 30, large)-net in base 16, because
- 6 times m-reduction [i] would yield (22, 24, large)-net in base 16, but