Best Known (97, 97+10, s)-Nets in Base 4
(97, 97+10, 1685911)-Net over F4 — Constructive and digital
Digital (97, 107, 1685911)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (17, 22, 8191)-net over F4, using
- net defined by OOA [i] based on linear OOA(422, 8191, F4, 5, 5) (dual of [(8191, 5), 40933, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(422, 16383, F4, 5) (dual of [16383, 16361, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(422, 16384, F4, 5) (dual of [16384, 16362, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(422, 16384, F4, 5) (dual of [16384, 16362, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(422, 16383, F4, 5) (dual of [16383, 16361, 6]-code), using
- net defined by OOA [i] based on linear OOA(422, 8191, F4, 5, 5) (dual of [(8191, 5), 40933, 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 (17, 22, 8191)-net over F4, using
(97, 97+10, large)-Net over F4 — Digital
Digital (97, 107, large)-net over F4, using
- 44 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
(97, 97+10, large)-Net in Base 4 — Upper bound on s
There is no (97, 107, large)-net in base 4, because
- 8 times m-reduction [i] would yield (97, 99, large)-net in base 4, but