Best Known (144, 144+14, s)-Nets in Base 4
(144, 144+14, 2396742)-Net over F4 — Constructive and digital
Digital (144, 158, 2396742)-net over F4, using
- trace code for nets [i] based on digital (65, 79, 1198371)-net over F16, using
- net defined by OOA [i] based on linear OOA(1679, 1198371, F16, 14, 14) (dual of [(1198371, 14), 16777115, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(1679, 8388597, F16, 14) (dual of [8388597, 8388518, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(1679, large, F16, 14) (dual of [large, large−79, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(1679, large, F16, 14) (dual of [large, large−79, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(1679, 8388597, F16, 14) (dual of [8388597, 8388518, 15]-code), using
- net defined by OOA [i] based on linear OOA(1679, 1198371, F16, 14, 14) (dual of [(1198371, 14), 16777115, 15]-NRT-code), using
(144, 144+14, large)-Net over F4 — Digital
Digital (144, 158, large)-net over F4, using
- 43 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
(144, 144+14, large)-Net in Base 4 — Upper bound on s
There is no (144, 158, large)-net in base 4, because
- 12 times m-reduction [i] would yield (144, 146, large)-net in base 4, but