Best Known (33, 49, s)-Nets in Base 16
(33, 49, 1028)-Net over F16 — Constructive and digital
Digital (33, 49, 1028)-net over F16, using
- 1 times m-reduction [i] based on digital (33, 50, 1028)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (8, 16, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 8, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 8, 257)-net over F256, using
- digital (17, 34, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 17, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- trace code for nets [i] based on digital (0, 17, 257)-net over F256, using
- digital (8, 16, 514)-net over F16, using
- (u, u+v)-construction [i] based on
(33, 49, 4257)-Net over F16 — Digital
Digital (33, 49, 4257)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1649, 4257, F16, 16) (dual of [4257, 4208, 17]-code), using
- 158 step Varšamov–Edel lengthening with (ri) = (2, 6 times 0, 1, 31 times 0, 1, 118 times 0) [i] based on linear OA(1645, 4095, F16, 16) (dual of [4095, 4050, 17]-code), using
- 1 times truncation [i] based on linear OA(1646, 4096, F16, 17) (dual of [4096, 4050, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 1 times truncation [i] based on linear OA(1646, 4096, F16, 17) (dual of [4096, 4050, 18]-code), using
- 158 step Varšamov–Edel lengthening with (ri) = (2, 6 times 0, 1, 31 times 0, 1, 118 times 0) [i] based on linear OA(1645, 4095, F16, 16) (dual of [4095, 4050, 17]-code), using
(33, 49, 5954336)-Net in Base 16 — Upper bound on s
There is no (33, 49, 5954337)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 100433 636988 547397 274409 549646 512677 897519 578264 246532 854716 > 1649 [i]