Best Known (108−24, 108, s)-Nets in Base 16
(108−24, 108, 10956)-Net over F16 — Constructive and digital
Digital (84, 108, 10956)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (2, 14, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-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 (2, 14, 33)-net over F16, using
(108−24, 108, 21846)-Net in Base 16 — Constructive
(84, 108, 21846)-net in base 16, using
- base change [i] based on digital (48, 72, 21846)-net over F64, using
- net defined by OOA [i] based on linear OOA(6472, 21846, F64, 24, 24) (dual of [(21846, 24), 524232, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(6472, 262152, F64, 24) (dual of [262152, 262080, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(6472, 262155, F64, 24) (dual of [262155, 262083, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] 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]
- linear OA(6461, 262144, F64, 21) (dual of [262144, 262083, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(642, 11, F64, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(6472, 262155, F64, 24) (dual of [262155, 262083, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(6472, 262152, F64, 24) (dual of [262152, 262080, 25]-code), using
- net defined by OOA [i] based on linear OOA(6472, 21846, F64, 24, 24) (dual of [(21846, 24), 524232, 25]-NRT-code), using
(108−24, 108, 283473)-Net over F16 — Digital
Digital (84, 108, 283473)-net over F16, using
(108−24, 108, large)-Net in Base 16 — Upper bound on s
There is no (84, 108, large)-net in base 16, because
- 22 times m-reduction [i] would yield (84, 86, large)-net in base 16, but