Best Known (112, 132, s)-Nets in Base 4
(112, 132, 6563)-Net over F4 — Constructive and digital
Digital (112, 132, 6563)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (2, 12, 10)-net over F4, using
- net from sequence [i] based on digital (2, 9)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 2 and N(F) ≥ 10, using
- net from sequence [i] based on digital (2, 9)-sequence over F4, using
- digital (100, 120, 6553)-net over F4, using
- net defined by OOA [i] based on linear OOA(4120, 6553, F4, 20, 20) (dual of [(6553, 20), 130940, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(4120, 65530, F4, 20) (dual of [65530, 65410, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4120, 65535, F4, 20) (dual of [65535, 65415, 21]-code), using
- 1 times truncation [i] based on linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 1 times truncation [i] based on linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4120, 65535, F4, 20) (dual of [65535, 65415, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(4120, 65530, F4, 20) (dual of [65530, 65410, 21]-code), using
- net defined by OOA [i] based on linear OOA(4120, 6553, F4, 20, 20) (dual of [(6553, 20), 130940, 21]-NRT-code), using
- digital (2, 12, 10)-net over F4, using
(112, 132, 60613)-Net over F4 — Digital
Digital (112, 132, 60613)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4132, 60613, F4, 20) (dual of [60613, 60481, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4132, 65558, F4, 20) (dual of [65558, 65426, 21]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(4129, 65537, F4, 21) (dual of [65537, 65408, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(497, 65537, F4, 17) (dual of [65537, 65440, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4132, 65558, F4, 20) (dual of [65558, 65426, 21]-code), using
(112, 132, large)-Net in Base 4 — Upper bound on s
There is no (112, 132, large)-net in base 4, because
- 18 times m-reduction [i] would yield (112, 114, large)-net in base 4, but