Best Known (30, 50, s)-Nets in Base 9
(30, 50, 320)-Net over F9 — Constructive and digital
Digital (30, 50, 320)-net over F9, using
- trace code for nets [i] based on digital (5, 25, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
(30, 50, 335)-Net over F9 — Digital
Digital (30, 50, 335)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(950, 335, F9, 20) (dual of [335, 285, 21]-code), using
- 25 step Varšamov–Edel lengthening with (ri) = (1, 4 times 0, 1, 19 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
- 25 step Varšamov–Edel lengthening with (ri) = (1, 4 times 0, 1, 19 times 0) [i] based on linear OA(948, 308, F9, 20) (dual of [308, 260, 21]-code), using
(30, 50, 33421)-Net in Base 9 — Upper bound on s
There is no (30, 50, 33422)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 515475 764503 408892 643242 135307 923481 761218 279841 > 950 [i]