Best Known (106−10, 106, s)-Nets in Base 4
(106−10, 106, 1683769)-Net over F4 — Constructive and digital
Digital (96, 106, 1683769)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (16, 21, 6049)-net over F4, using
- net defined by OOA [i] based on linear OOA(421, 6049, F4, 5, 5) (dual of [(6049, 5), 30224, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(421, 12099, F4, 5) (dual of [12099, 12078, 6]-code), using
- trace code [i] based on linear OA(647, 4033, F64, 5) (dual of [4033, 4026, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(421, 12099, F4, 5) (dual of [12099, 12078, 6]-code), using
- net defined by OOA [i] based on linear OOA(421, 6049, F4, 5, 5) (dual of [(6049, 5), 30224, 6]-NRT-code), using
- digital (75, 85, 1677720)-net over F4, using
- net defined by OOA [i] based on linear OOA(485, 1677720, F4, 10, 10) (dual of [(1677720, 10), 16777115, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(485, 8388600, F4, 10) (dual of [8388600, 8388515, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(485, large, F4, 10) (dual of [large, large−85, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(485, large, F4, 10) (dual of [large, large−85, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(485, 8388600, F4, 10) (dual of [8388600, 8388515, 11]-code), using
- net defined by OOA [i] based on linear OOA(485, 1677720, F4, 10, 10) (dual of [(1677720, 10), 16777115, 11]-NRT-code), using
- digital (16, 21, 6049)-net over F4, using
(106−10, 106, large)-Net over F4 — Digital
Digital (96, 106, large)-net over F4, using
- 43 times duplication [i] based on digital (93, 103, large)-net over F4, using
- t-expansion [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
- t-expansion [i] based on digital (92, 103, large)-net over F4, using
(106−10, 106, large)-Net in Base 4 — Upper bound on s
There is no (96, 106, large)-net in base 4, because
- 8 times m-reduction [i] would yield (96, 98, large)-net in base 4, but