Best Known (97−42, 97, s)-Nets in Base 4
(97−42, 97, 130)-Net over F4 — Constructive and digital
Digital (55, 97, 130)-net over F4, using
- 1 times m-reduction [i] based on digital (55, 98, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 49, 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
- trace code for nets [i] based on digital (6, 49, 65)-net over F16, using
(97−42, 97, 1730)-Net in Base 4 — Upper bound on s
There is no (55, 97, 1731)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 25365 345039 586015 665113 309174 184545 737997 326492 507359 304096 > 497 [i]