Best Known (25, 25+86, s)-Nets in Base 16
(25, 25+86, 65)-Net over F16 — Constructive and digital
Digital (25, 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
(25, 25+86, 66)-Net in Base 16 — Constructive
(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
(25, 25+86, 144)-Net over F16 — Digital
Digital (25, 111, 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
(25, 25+86, 1420)-Net in Base 16 — Upper bound on s
There is no (25, 111, 1421)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 45 931899 069156 724109 879004 973563 506033 523583 606873 330138 855682 677069 706272 246792 485008 985046 590890 043896 519695 294343 182596 384421 942096 > 16111 [i]