Best Known (143, 143+14, s)-Nets in Base 4
(143, 143+14, 1203834)-Net over F4 — Constructive and digital
Digital (143, 157, 1203834)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (29, 36, 5463)-net over F4, using
- net defined by OOA [i] based on linear OOA(436, 5463, F4, 7, 7) (dual of [(5463, 7), 38205, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(436, 16390, F4, 7) (dual of [16390, 16354, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(436, 16391, F4, 7) (dual of [16391, 16355, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(436, 16384, F4, 7) (dual of [16384, 16348, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(429, 16384, F4, 6) (dual of [16384, 16355, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(40, 7, F4, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(436, 16391, F4, 7) (dual of [16391, 16355, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(436, 16390, F4, 7) (dual of [16390, 16354, 8]-code), using
- net defined by OOA [i] based on linear OOA(436, 5463, F4, 7, 7) (dual of [(5463, 7), 38205, 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 (29, 36, 5463)-net over F4, using
(143, 143+14, large)-Net over F4 — Digital
Digital (143, 157, large)-net over F4, using
- 42 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
(143, 143+14, large)-Net in Base 4 — Upper bound on s
There is no (143, 157, large)-net in base 4, because
- 12 times m-reduction [i] would yield (143, 145, large)-net in base 4, but