Best Known (82, 106, s)-Nets in Base 16
(82, 106, 10940)-Net over F16 — Constructive and digital
Digital (82, 106, 10940)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (0, 12, 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 (70, 94, 10923)-net over F16, using
- net defined by OOA [i] based on linear OOA(1694, 10923, F16, 24, 24) (dual of [(10923, 24), 262058, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(1694, 131076, F16, 24) (dual of [131076, 130982, 25]-code), using
- trace code [i] based on linear OA(25647, 65538, F256, 24) (dual of [65538, 65491, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- trace code [i] based on linear OA(25647, 65538, F256, 24) (dual of [65538, 65491, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(1694, 131076, F16, 24) (dual of [131076, 130982, 25]-code), using
- net defined by OOA [i] based on linear OOA(1694, 10923, F16, 24, 24) (dual of [(10923, 24), 262058, 25]-NRT-code), using
- digital (0, 12, 17)-net over F16, using
(82, 106, 21845)-Net in Base 16 — Constructive
(82, 106, 21845)-net in base 16, using
- 161 times duplication [i] based on (81, 105, 21845)-net in base 16, using
- base change [i] based on digital (46, 70, 21845)-net over F64, using
- net defined by OOA [i] based on linear OOA(6470, 21845, F64, 24, 24) (dual of [(21845, 24), 524210, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(6470, 262140, F64, 24) (dual of [262140, 262070, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(6470, 262144, F64, 24) (dual of [262144, 262074, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(6470, 262144, F64, 24) (dual of [262144, 262074, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(6470, 262140, F64, 24) (dual of [262140, 262070, 25]-code), using
- net defined by OOA [i] based on linear OOA(6470, 21845, F64, 24, 24) (dual of [(21845, 24), 524210, 25]-NRT-code), using
- base change [i] based on digital (46, 70, 21845)-net over F64, using
(82, 106, 222746)-Net over F16 — Digital
Digital (82, 106, 222746)-net over F16, using
(82, 106, large)-Net in Base 16 — Upper bound on s
There is no (82, 106, large)-net in base 16, because
- 22 times m-reduction [i] would yield (82, 84, large)-net in base 16, but