Best Known (90, 90+10, s)-Nets in Base 4
(90, 90+10, 1677961)-Net over F4 — Constructive and digital
Digital (90, 100, 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 (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 (10, 15, 241)-net over F4, using
(90, 90+10, large)-Net over F4 — Digital
Digital (90, 100, large)-net over F4, using
- 48 times duplication [i] based on digital (82, 92, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(492, large, F4, 10) (dual of [large, large−92, 11]-code), using
- 7 times code embedding in larger space [i] 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]
- 7 times code embedding in larger space [i] based on linear OA(485, large, F4, 10) (dual of [large, large−85, 11]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(492, large, F4, 10) (dual of [large, large−92, 11]-code), using
(90, 90+10, large)-Net in Base 4 — Upper bound on s
There is no (90, 100, large)-net in base 4, because
- 8 times m-reduction [i] would yield (90, 92, large)-net in base 4, but