Best Known (41−16, 41, s)-Nets in Base 9
(41−16, 41, 300)-Net over F9 — Constructive and digital
Digital (25, 41, 300)-net over F9, using
- 1 times m-reduction [i] based on digital (25, 42, 300)-net over F9, using
- trace code for nets [i] based on digital (4, 21, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- trace code for nets [i] based on digital (4, 21, 150)-net over F81, using
(41−16, 41, 337)-Net over F9 — Digital
Digital (25, 41, 337)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(941, 337, F9, 16) (dual of [337, 296, 17]-code), using
- 28 step Varšamov–Edel lengthening with (ri) = (1, 27 times 0) [i] based on linear OA(940, 308, F9, 16) (dual of [308, 268, 17]-code), using
- trace code [i] based on linear OA(8120, 154, F81, 16) (dual of [154, 134, 17]-code), using
- extended algebraic-geometric code AGe(F,137P) [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 154, using
- trace code [i] based on linear OA(8120, 154, F81, 16) (dual of [154, 134, 17]-code), using
- 28 step Varšamov–Edel lengthening with (ri) = (1, 27 times 0) [i] based on linear OA(940, 308, F9, 16) (dual of [308, 268, 17]-code), using
(41−16, 41, 36562)-Net in Base 9 — Upper bound on s
There is no (25, 41, 36563)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 1330 336527 942505 786126 231512 325612 324545 > 941 [i]