Best Known (29, 29+20, s)-Nets in Base 9
(29, 29+20, 300)-Net over F9 — Constructive and digital
Digital (29, 49, 300)-net over F9, using
- 1 times m-reduction [i] based on digital (29, 50, 300)-net over F9, using
- trace code for nets [i] based on digital (4, 25, 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, 25, 150)-net over F81, using
(29, 29+20, 314)-Net over F9 — Digital
Digital (29, 49, 314)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(949, 314, F9, 20) (dual of [314, 265, 21]-code), using
- 5 step Varšamov–Edel lengthening with (ri) = (1, 4 times 0) [i] based on linear OA(948, 308, F9, 20) (dual of [308, 260, 21]-code), using
- trace code [i] based on linear OA(8124, 154, F81, 20) (dual of [154, 130, 21]-code), using
- extended algebraic-geometric code AGe(F,133P) [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 154, using
- trace code [i] based on linear OA(8124, 154, F81, 20) (dual of [154, 130, 21]-code), using
- 5 step Varšamov–Edel lengthening with (ri) = (1, 4 times 0) [i] based on linear OA(948, 308, F9, 20) (dual of [308, 260, 21]-code), using
(29, 29+20, 26827)-Net in Base 9 — Upper bound on s
There is no (29, 49, 26828)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 57273 070504 931606 362101 677920 463678 481687 086401 > 949 [i]