Best Known (13, 89, s)-Nets in Base 16
(13, 89, 65)-Net over F16 — Constructive and digital
Digital (13, 89, 65)-net over F16, using
- t-expansion [i] based on digital (6, 89, 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
(13, 89, 97)-Net over F16 — Digital
Digital (13, 89, 97)-net over F16, using
- net from sequence [i] based on digital (13, 96)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 13 and N(F) ≥ 97, using
(13, 89, 641)-Net in Base 16 — Upper bound on s
There is no (13, 89, 642)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 153883 940089 464001 581340 802873 805527 650045 429300 542942 666725 214088 013648 187811 094773 517258 930208 711813 025216 > 1689 [i]