Best Known (70−16, 70, s)-Nets in Base 16
(70−16, 70, 16401)-Net over F16 — Constructive and digital
Digital (54, 70, 16401)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 16)-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 (0, 8, 17)-net over F16, using
(70−16, 70, 32768)-Net in Base 16 — Constructive
(54, 70, 32768)-net in base 16, using
- 161 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
(70−16, 70, 178205)-Net over F16 — Digital
Digital (54, 70, 178205)-net over F16, using
(70−16, 70, large)-Net in Base 16 — Upper bound on s
There is no (54, 70, large)-net in base 16, because
- 14 times m-reduction [i] would yield (54, 56, large)-net in base 16, but