Best Known (40−16, 40, s)-Nets in Base 16
(40−16, 40, 531)-Net over F16 — Constructive and digital
Digital (24, 40, 531)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- digital (16, 32, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 16, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 16, 257)-net over F256, using
- digital (0, 8, 17)-net over F16, using
(40−16, 40, 730)-Net over F16 — Digital
Digital (24, 40, 730)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1640, 730, F16, 16) (dual of [730, 690, 17]-code), using
- 84 step Varšamov–Edel lengthening with (ri) = (2, 4 times 0, 1, 19 times 0, 1, 58 times 0) [i] based on linear OA(1636, 642, F16, 16) (dual of [642, 606, 17]-code), using
- trace code [i] based on linear OA(25618, 321, F256, 16) (dual of [321, 303, 17]-code), using
- extended algebraic-geometric code AGe(F,304P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25618, 321, F256, 16) (dual of [321, 303, 17]-code), using
- 84 step Varšamov–Edel lengthening with (ri) = (2, 4 times 0, 1, 19 times 0, 1, 58 times 0) [i] based on linear OA(1636, 642, F16, 16) (dual of [642, 606, 17]-code), using
(40−16, 40, 263143)-Net in Base 16 — Upper bound on s
There is no (24, 40, 263144)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 1 461539 568934 449785 456785 157332 184278 112270 416156 > 1640 [i]