Best Known (117−90, 117, s)-Nets in Base 16
(117−90, 117, 65)-Net over F16 — Constructive and digital
Digital (27, 117, 65)-net over F16, using
- t-expansion [i] based on digital (6, 117, 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
(117−90, 117, 66)-Net in Base 16 — Constructive
(27, 117, 66)-net in base 16, using
- t-expansion [i] based on (25, 117, 66)-net in base 16, using
- net from sequence [i] based on (25, 65)-sequence in base 16, using
- base expansion [i] based on digital (50, 65)-sequence over F4, using
- t-expansion [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- t-expansion [i] based on digital (49, 65)-sequence over F4, using
- base expansion [i] based on digital (50, 65)-sequence over F4, using
- net from sequence [i] based on (25, 65)-sequence in base 16, using
(117−90, 117, 156)-Net over F16 — Digital
Digital (27, 117, 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
(117−90, 117, 1562)-Net in Base 16 — Upper bound on s
There is no (27, 117, 1563)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 764 492868 997578 029344 949127 142970 812835 032232 592099 911677 358100 290474 027069 160661 973961 996354 620511 393724 832957 805412 233893 992115 337532 187776 > 16117 [i]