Best Known (7, 7+36, s)-Nets in Base 16
(7, 7+36, 65)-Net over F16 — Constructive and digital
Digital (7, 43, 65)-net over F16, using
- t-expansion [i] based on digital (6, 43, 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
(7, 7+36, 369)-Net in Base 16 — Upper bound on s
There is no (7, 43, 370)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 6193 292331 819747 248598 609890 723338 806761 816669 369776 > 1643 [i]