Best Known (69−28, 69, s)-Nets in Base 9
(69−28, 69, 320)-Net over F9 — Constructive and digital
Digital (41, 69, 320)-net over F9, using
- 3 times m-reduction [i] based on digital (41, 72, 320)-net over F9, using
- trace code for nets [i] based on digital (5, 36, 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, 36, 160)-net over F81, using
(69−28, 69, 394)-Net over F9 — Digital
Digital (41, 69, 394)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(969, 394, F9, 28) (dual of [394, 325, 29]-code), using
- 13 step Varšamov–Edel lengthening with (ri) = (1, 12 times 0) [i] based on linear OA(968, 380, F9, 28) (dual of [380, 312, 29]-code), using
- trace code [i] based on linear OA(8134, 190, F81, 28) (dual of [190, 156, 29]-code), using
- extended algebraic-geometric code AGe(F,161P) [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- trace code [i] based on linear OA(8134, 190, F81, 28) (dual of [190, 156, 29]-code), using
- 13 step Varšamov–Edel lengthening with (ri) = (1, 12 times 0) [i] based on linear OA(968, 380, F9, 28) (dual of [380, 312, 29]-code), using
(69−28, 69, 38135)-Net in Base 9 — Upper bound on s
There is no (41, 69, 38136)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 696399 579488 604105 566056 379500 687832 112387 281355 600988 812656 028033 > 969 [i]