Best Known (54−28, 54, s)-Nets in Base 16
(54−28, 54, 130)-Net over F16 — Constructive and digital
Digital (26, 54, 130)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 20, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- digital (6, 34, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16 (see above)
- digital (6, 20, 65)-net over F16, using
(54−28, 54, 177)-Net in Base 16 — Constructive
(26, 54, 177)-net in base 16, using
- 3 times m-reduction [i] based on (26, 57, 177)-net in base 16, using
- base change [i] based on digital (7, 38, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- base change [i] based on digital (7, 38, 177)-net over F64, using
(54−28, 54, 190)-Net over F16 — Digital
Digital (26, 54, 190)-net over F16, using
(54−28, 54, 17768)-Net in Base 16 — Upper bound on s
There is no (26, 54, 17769)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 105364 374250 898248 815966 317810 143333 379324 000001 098066 060956 473616 > 1654 [i]