Best Known (44−36, 44, s)-Nets in Base 16
(44−36, 44, 65)-Net over F16 — Constructive and digital
Digital (8, 44, 65)-net over F16, using
- t-expansion [i] based on digital (6, 44, 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
(44−36, 44, 432)-Net in Base 16 — Upper bound on s
There is no (8, 44, 433)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 98244 416849 794320 652374 828074 987033 617418 821195 504336 > 1644 [i]