Best Known (111−84, 111, s)-Nets in Base 16
(111−84, 111, 65)-Net over F16 — Constructive and digital
Digital (27, 111, 65)-net over F16, using
- t-expansion [i] based on digital (6, 111, 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
(111−84, 111, 66)-Net in Base 16 — Constructive
(27, 111, 66)-net in base 16, using
- t-expansion [i] based on (25, 111, 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
(111−84, 111, 156)-Net over F16 — Digital
Digital (27, 111, 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
(111−84, 111, 1651)-Net in Base 16 — Upper bound on s
There is no (27, 111, 1652)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 45 621708 310323 618830 068617 300202 353046 884715 418039 578830 268531 205313 552258 864130 712180 140269 199320 154314 978729 046358 261541 469238 308186 > 16111 [i]