Best Known (55, 71, s)-Nets in Base 16
(55, 71, 16408)-Net over F16 — Constructive and digital
Digital (55, 71, 16408)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 24)-net over F16, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- digital (46, 62, 16384)-net over F16, using
- net defined by OOA [i] based on linear OOA(1662, 16384, F16, 16, 16) (dual of [(16384, 16), 262082, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(1662, 131072, F16, 16) (dual of [131072, 131010, 17]-code), using
- trace code [i] based on linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- trace code [i] based on linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(1662, 131072, F16, 16) (dual of [131072, 131010, 17]-code), using
- net defined by OOA [i] based on linear OOA(1662, 16384, F16, 16, 16) (dual of [(16384, 16), 262082, 17]-NRT-code), using
- digital (1, 9, 24)-net over F16, using
(55, 71, 32768)-Net in Base 16 — Constructive
(55, 71, 32768)-net in base 16, using
- 162 times duplication [i] based on (53, 69, 32768)-net in base 16, using
- base change [i] based on digital (30, 46, 32768)-net over F64, using
- net defined by OOA [i] based on linear OOA(6446, 32768, F64, 16, 16) (dual of [(32768, 16), 524242, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(6446, 262144, F64, 16) (dual of [262144, 262098, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- OA 8-folding and stacking [i] based on linear OA(6446, 262144, F64, 16) (dual of [262144, 262098, 17]-code), using
- net defined by OOA [i] based on linear OOA(6446, 32768, F64, 16, 16) (dual of [(32768, 16), 524242, 17]-NRT-code), using
- base change [i] based on digital (30, 46, 32768)-net over F64, using
(55, 71, 214384)-Net over F16 — Digital
Digital (55, 71, 214384)-net over F16, using
(55, 71, large)-Net in Base 16 — Upper bound on s
There is no (55, 71, large)-net in base 16, because
- 14 times m-reduction [i] would yield (55, 57, large)-net in base 16, but