Best Known (112−86, 112, s)-Nets in Base 16
(112−86, 112, 65)-Net over F16 — Constructive and digital
Digital (26, 112, 65)-net over F16, using
- t-expansion [i] based on digital (6, 112, 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
(112−86, 112, 66)-Net in Base 16 — Constructive
(26, 112, 66)-net in base 16, using
- t-expansion [i] based on (25, 112, 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
(112−86, 112, 150)-Net over F16 — Digital
Digital (26, 112, 150)-net over F16, using
- net from sequence [i] based on digital (26, 149)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 26 and N(F) ≥ 150, using
(112−86, 112, 1516)-Net in Base 16 — Upper bound on s
There is no (26, 112, 1517)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 730 414296 704048 864002 061447 027883 369883 268070 121293 122262 877746 442545 080542 541591 203012 952707 053510 420206 961166 194533 728239 281319 437116 > 16112 [i]