Best Known (37, 77, s)-Nets in Base 16
(37, 77, 130)-Net over F16 — Constructive and digital
Digital (37, 77, 130)-net over F16, using
- 10 times m-reduction [i] based on digital (37, 87, 130)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 31, 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, 56, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16 (see above)
- digital (6, 31, 65)-net over F16, using
- (u, u+v)-construction [i] based on
(37, 77, 192)-Net in Base 16 — Constructive
(37, 77, 192)-net in base 16, using
- t-expansion [i] based on (36, 77, 192)-net in base 16, using
- base change [i] based on digital (3, 44, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 44, 192)-net over F128, using
(37, 77, 241)-Net over F16 — Digital
Digital (37, 77, 241)-net over F16, using
(37, 77, 23926)-Net in Base 16 — Upper bound on s
There is no (37, 77, 23927)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 521 671228 863286 991812 365931 092496 120244 041103 076761 602305 605334 910796 697812 158675 587171 890101 > 1677 [i]