Best Known (49−43, 49, s)-Nets in Base 16
(49−43, 49, 65)-Net over F16 — Constructive and digital
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
(49−43, 49, 314)-Net in Base 16 — Upper bound on s
There is no (6, 49, 315)-net in base 16, because
- 3 times m-reduction [i] would yield (6, 46, 315)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 24 726728 512693 579650 694589 507267 266161 522188 191716 002626 > 1646 [i]