Best Known (80−62, 80, s)-Nets in Base 16
(80−62, 80, 65)-Net over F16 — Constructive and digital
Digital (18, 80, 65)-net over F16, using
- t-expansion [i] based on digital (6, 80, 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
(80−62, 80, 113)-Net over F16 — Digital
Digital (18, 80, 113)-net over F16, using
- net from sequence [i] based on digital (18, 112)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 18 and N(F) ≥ 113, using
(80−62, 80, 1043)-Net in Base 16 — Upper bound on s
There is no (18, 80, 1044)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 2 192604 405327 999221 691743 243673 528494 872523 932252 351111 654566 310164 156917 390534 886606 788940 142336 > 1680 [i]