Best Known (73−30, 73, s)-Nets in Base 9
(73−30, 73, 320)-Net over F9 — Constructive and digital
Digital (43, 73, 320)-net over F9, using
- 3 times m-reduction [i] based on digital (43, 76, 320)-net over F9, using
- trace code for nets [i] based on digital (5, 38, 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
- trace code for nets [i] based on digital (5, 38, 160)-net over F81, using
(73−30, 73, 387)-Net over F9 — Digital
Digital (43, 73, 387)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(973, 387, F9, 30) (dual of [387, 314, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(973, 390, F9, 30) (dual of [390, 317, 31]-code), using
- 9 step Varšamov–Edel lengthening with (ri) = (1, 8 times 0) [i] based on linear OA(972, 380, F9, 30) (dual of [380, 308, 31]-code), using
- trace code [i] based on linear OA(8136, 190, F81, 30) (dual of [190, 154, 31]-code), using
- extended algebraic-geometric code AGe(F,159P) [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- trace code [i] based on linear OA(8136, 190, F81, 30) (dual of [190, 154, 31]-code), using
- 9 step Varšamov–Edel lengthening with (ri) = (1, 8 times 0) [i] based on linear OA(972, 380, F9, 30) (dual of [380, 308, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(973, 390, F9, 30) (dual of [390, 317, 31]-code), using
(73−30, 73, 35362)-Net in Base 9 — Upper bound on s
There is no (43, 73, 35363)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 4567 949482 015794 806905 062357 470896 208246 817582 272182 854629 373317 723625 > 973 [i]