Best Known (29, 29+94, s)-Nets in Base 16
(29, 29+94, 65)-Net over F16 — Constructive and digital
Digital (29, 123, 65)-net over F16, using
- t-expansion [i] based on digital (6, 123, 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
(29, 29+94, 66)-Net in Base 16 — Constructive
(29, 123, 66)-net in base 16, using
- t-expansion [i] based on (25, 123, 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
(29, 29+94, 161)-Net over F16 — Digital
Digital (29, 123, 161)-net over F16, using
- net from sequence [i] based on digital (29, 160)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 29 and N(F) ≥ 161, using
(29, 29+94, 1708)-Net in Base 16 — Upper bound on s
There is no (29, 123, 1709)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 12915 931984 411771 753401 122538 541318 660421 931625 548408 035717 346260 500298 424366 079858 012615 307211 388741 361582 938870 886455 943491 391561 429185 042958 068096 > 16123 [i]