Best Known (65−26, 65, s)-Nets in Base 9
(65−26, 65, 320)-Net over F9 — Constructive and digital
Digital (39, 65, 320)-net over F9, using
- 3 times m-reduction [i] based on digital (39, 68, 320)-net over F9, using
- trace code for nets [i] based on digital (5, 34, 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, 34, 160)-net over F81, using
(65−26, 65, 400)-Net over F9 — Digital
Digital (39, 65, 400)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(965, 400, F9, 26) (dual of [400, 335, 27]-code), using
- 19 step Varšamov–Edel lengthening with (ri) = (1, 18 times 0) [i] based on linear OA(964, 380, F9, 26) (dual of [380, 316, 27]-code), using
- trace code [i] based on linear OA(8132, 190, F81, 26) (dual of [190, 158, 27]-code), using
- extended algebraic-geometric code AGe(F,163P) [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- trace code [i] based on linear OA(8132, 190, F81, 26) (dual of [190, 158, 27]-code), using
- 19 step Varšamov–Edel lengthening with (ri) = (1, 18 times 0) [i] based on linear OA(964, 380, F9, 26) (dual of [380, 316, 27]-code), using
(65−26, 65, 41826)-Net in Base 9 — Upper bound on s
There is no (39, 65, 41827)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 106 134334 605080 606979 471181 341824 415261 461235 392992 436531 041593 > 965 [i]