Best Known (116−90, 116, s)-Nets in Base 16
(116−90, 116, 65)-Net over F16 — Constructive and digital
Digital (26, 116, 65)-net over F16, using
- t-expansion [i] based on digital (6, 116, 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
(116−90, 116, 66)-Net in Base 16 — Constructive
(26, 116, 66)-net in base 16, using
- t-expansion [i] based on (25, 116, 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
(116−90, 116, 150)-Net over F16 — Digital
Digital (26, 116, 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
(116−90, 116, 1468)-Net in Base 16 — Upper bound on s
There is no (26, 116, 1469)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 49 059524 531197 208539 581692 691634 023495 376036 223011 570217 033380 206894 381890 301672 103065 083711 870130 198430 196384 580644 393467 244519 892665 176576 > 16116 [i]