Best Known (27, 27+77, s)-Nets in Base 16
(27, 27+77, 65)-Net over F16 — Constructive and digital
Digital (27, 104, 65)-net over F16, using
- t-expansion [i] based on digital (6, 104, 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
(27, 27+77, 76)-Net in Base 16 — Constructive
(27, 104, 76)-net in base 16, using
- 6 times m-reduction [i] based on (27, 110, 76)-net in base 16, using
- base change [i] based on digital (5, 88, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- base change [i] based on digital (5, 88, 76)-net over F32, using
(27, 27+77, 156)-Net over F16 — Digital
Digital (27, 104, 156)-net over F16, using
- net from sequence [i] based on digital (27, 155)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 27 and N(F) ≥ 156, using
(27, 27+77, 1817)-Net in Base 16 — Upper bound on s
There is no (27, 104, 1818)-net in base 16, because
- 1 times m-reduction [i] would yield (27, 103, 1818)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 10636 938490 893382 475370 122948 405157 854262 840228 138927 767919 253977 937392 936655 029204 001462 823948 722603 289560 388680 166672 827936 > 16103 [i]