Best Known (25−14, 25, s)-Nets in Base 16
(25−14, 25, 66)-Net over F16 — Constructive and digital
Digital (11, 25, 66)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (2, 9, 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 (2, 16, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16 (see above)
- digital (2, 9, 33)-net over F16, using
(25−14, 25, 86)-Net over F16 — Digital
Digital (11, 25, 86)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1625, 86, F16, 14) (dual of [86, 61, 15]-code), using
- an extension Ce(13) of the narrow-sense BCH-code C(I) with length 85 | 162−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
(25−14, 25, 129)-Net in Base 16 — Constructive
(11, 25, 129)-net in base 16, using
- base change [i] based on (6, 20, 129)-net in base 32, using
- 1 times m-reduction [i] based on (6, 21, 129)-net in base 32, using
- base change [i] based on digital (0, 15, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- base change [i] based on digital (0, 15, 129)-net over F128, using
- 1 times m-reduction [i] based on (6, 21, 129)-net in base 32, using
(25−14, 25, 4496)-Net in Base 16 — Upper bound on s
There is no (11, 25, 4497)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 1 267682 801683 998385 821011 430736 > 1625 [i]