Best Known (156−16, 156, s)-Nets in Base 4
(156−16, 156, 1048592)-Net over F4 — Constructive and digital
Digital (140, 156, 1048592)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (4, 12, 17)-net over F4, using
- digital (128, 144, 1048575)-net over F4, using
- net defined by OOA [i] based on linear OOA(4144, 1048575, F4, 16, 16) (dual of [(1048575, 16), 16777056, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(4144, 8388600, F4, 16) (dual of [8388600, 8388456, 17]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(4144, large, F4, 16) (dual of [large, large−144, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(4144, 8388600, F4, 16) (dual of [8388600, 8388456, 17]-code), using
- net defined by OOA [i] based on linear OOA(4144, 1048575, F4, 16, 16) (dual of [(1048575, 16), 16777056, 17]-NRT-code), using
(156−16, 156, large)-Net over F4 — Digital
Digital (140, 156, large)-net over F4, using
- 41 times duplication [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
(156−16, 156, large)-Net in Base 4 — Upper bound on s
There is no (140, 156, large)-net in base 4, because
- 14 times m-reduction [i] would yield (140, 142, large)-net in base 4, but