Best Known (71, 130, s)-Nets in Base 4
(71, 130, 130)-Net over F4 — Constructive and digital
Digital (71, 130, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 65, 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
(71, 130, 135)-Net over F4 — Digital
Digital (71, 130, 135)-net over F4, using
(71, 130, 1830)-Net in Base 4 — Upper bound on s
There is no (71, 130, 1831)-net in base 4, because
- 1 times m-reduction [i] would yield (71, 129, 1831)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 466556 314011 872671 140471 907307 040077 356798 596069 674574 588561 709213 569776 514328 > 4129 [i]