Best Known (107−82, 107, s)-Nets in Base 16
(107−82, 107, 65)-Net over F16 — Constructive and digital
Digital (25, 107, 65)-net over F16, using
- t-expansion [i] based on digital (6, 107, 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
(107−82, 107, 66)-Net in Base 16 — Constructive
(25, 107, 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
(107−82, 107, 144)-Net over F16 — Digital
Digital (25, 107, 144)-net over F16, using
- net from sequence [i] based on digital (25, 143)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 25 and N(F) ≥ 144, using
(107−82, 107, 1471)-Net in Base 16 — Upper bound on s
There is no (25, 107, 1472)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 710 243120 325400 850163 589218 483630 769550 482291 546954 671301 656734 314160 448485 784463 613979 248651 530813 402007 734846 537533 555185 325031 > 16107 [i]