Best Known (156−14, 156, s)-Nets in Base 4
(156−14, 156, 1200191)-Net over F4 — Constructive and digital
Digital (142, 156, 1200191)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (28, 35, 1820)-net over F4, using
- net defined by OOA [i] based on linear OOA(435, 1820, F4, 7, 7) (dual of [(1820, 7), 12705, 8]-NRT-code), using
- digital (107, 121, 1198371)-net over F4, using
- net defined by OOA [i] based on linear OOA(4121, 1198371, F4, 14, 14) (dual of [(1198371, 14), 16777073, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(4121, 8388597, F4, 14) (dual of [8388597, 8388476, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(4121, large, F4, 14) (dual of [large, large−121, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(4121, large, F4, 14) (dual of [large, large−121, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(4121, 8388597, F4, 14) (dual of [8388597, 8388476, 15]-code), using
- net defined by OOA [i] based on linear OOA(4121, 1198371, F4, 14, 14) (dual of [(1198371, 14), 16777073, 15]-NRT-code), using
- digital (28, 35, 1820)-net over F4, using
(156−14, 156, large)-Net over F4 — Digital
Digital (142, 156, large)-net over F4, using
- 41 times duplication [i] based on digital (141, 155, large)-net over F4, using
- t-expansion [i] based on digital (139, 155, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4155, large, F4, 16) (dual of [large, large−155, 17]-code), using
- 11 times code embedding in larger space [i] based on linear OA(4144, large, F4, 16) (dual of [large, large−144, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 11 times code embedding in larger space [i] based on linear OA(4144, large, F4, 16) (dual of [large, large−144, 17]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4155, large, F4, 16) (dual of [large, large−155, 17]-code), using
- t-expansion [i] based on digital (139, 155, large)-net over F4, using
(156−14, 156, large)-Net in Base 4 — Upper bound on s
There is no (142, 156, large)-net in base 4, because
- 12 times m-reduction [i] would yield (142, 144, large)-net in base 4, but