Best Known (25, 25+56, s)-Nets in Base 16
(25, 25+56, 65)-Net over F16 — Constructive and digital
Digital (25, 81, 65)-net over F16, using
- t-expansion [i] based on digital (6, 81, 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
(25, 25+56, 98)-Net in Base 16 — Constructive
(25, 81, 98)-net in base 16, using
- 9 times m-reduction [i] based on (25, 90, 98)-net in base 16, using
- base change [i] based on digital (7, 72, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- base change [i] based on digital (7, 72, 98)-net over F32, using
(25, 25+56, 144)-Net over F16 — Digital
Digital (25, 81, 144)-net over F16, using
- net from sequence [i] based on digital (25, 143)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 25 and N(F) ≥ 144, using
(25, 25+56, 2276)-Net in Base 16 — Upper bound on s
There is no (25, 81, 2277)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 34 216167 942497 365721 237487 211663 091128 744095 008724 764743 536126 090806 532263 909407 087432 499913 353116 > 1681 [i]