Best Known (88−62, 88, s)-Nets in Base 16
(88−62, 88, 65)-Net over F16 — Constructive and digital
Digital (26, 88, 65)-net over F16, using
- t-expansion [i] based on digital (6, 88, 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
(88−62, 88, 98)-Net in Base 16 — Constructive
(26, 88, 98)-net in base 16, using
- 7 times m-reduction [i] based on (26, 95, 98)-net in base 16, using
- base change [i] based on digital (7, 76, 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, 76, 98)-net over F32, using
(88−62, 88, 150)-Net over F16 — Digital
Digital (26, 88, 150)-net over F16, using
- net from sequence [i] based on digital (26, 149)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 26 and N(F) ≥ 150, using
(88−62, 88, 2151)-Net in Base 16 — Upper bound on s
There is no (26, 88, 2152)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 9290 916542 590296 613084 671815 306937 173459 971399 032480 560962 438687 176579 377086 358477 394186 367633 955008 959556 > 1688 [i]