Best Known (112−11, 112, s)-Nets in Base 4
(112−11, 112, 1677961)-Net over F4 — Constructive and digital
Digital (101, 112, 1677961)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (10, 15, 241)-net over F4, using
- net defined by OOA [i] based on linear OOA(415, 241, F4, 5, 5) (dual of [(241, 5), 1190, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(415, 483, F4, 5) (dual of [483, 468, 6]-code), using
- 1 times code embedding in larger space [i] based on linear OA(414, 482, F4, 5) (dual of [482, 468, 6]-code), using
- trace code [i] based on linear OA(167, 241, F16, 5) (dual of [241, 234, 6]-code), using
- 1 times code embedding in larger space [i] based on linear OA(414, 482, F4, 5) (dual of [482, 468, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(415, 483, F4, 5) (dual of [483, 468, 6]-code), using
- net defined by OOA [i] based on linear OOA(415, 241, F4, 5, 5) (dual of [(241, 5), 1190, 6]-NRT-code), using
- digital (86, 97, 1677720)-net over F4, using
- net defined by OOA [i] based on linear OOA(497, 1677720, F4, 11, 11) (dual of [(1677720, 11), 18454823, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(497, 8388601, F4, 11) (dual of [8388601, 8388504, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(497, large, F4, 11) (dual of [large, large−97, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(497, large, F4, 11) (dual of [large, large−97, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(497, 8388601, F4, 11) (dual of [8388601, 8388504, 12]-code), using
- net defined by OOA [i] based on linear OOA(497, 1677720, F4, 11, 11) (dual of [(1677720, 11), 18454823, 12]-NRT-code), using
- digital (10, 15, 241)-net over F4, using
(112−11, 112, large)-Net over F4 — Digital
Digital (101, 112, large)-net over F4, using
- 49 times duplication [i] based on digital (92, 103, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4103, large, F4, 11) (dual of [large, large−103, 12]-code), using
- 6 times code embedding in larger space [i] based on linear OA(497, large, F4, 11) (dual of [large, large−97, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- 6 times code embedding in larger space [i] based on linear OA(497, large, F4, 11) (dual of [large, large−97, 12]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4103, large, F4, 11) (dual of [large, large−103, 12]-code), using
(112−11, 112, large)-Net in Base 4 — Upper bound on s
There is no (101, 112, large)-net in base 4, because
- 9 times m-reduction [i] would yield (101, 103, large)-net in base 4, but