Best Known (53−21, 53, s)-Nets in Base 9
(53−21, 53, 320)-Net over F9 — Constructive and digital
Digital (32, 53, 320)-net over F9, using
- 1 times m-reduction [i] based on digital (32, 54, 320)-net over F9, using
- trace code for nets [i] based on digital (5, 27, 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, 27, 160)-net over F81, using
(53−21, 53, 362)-Net over F9 — Digital
Digital (32, 53, 362)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(953, 362, F9, 21) (dual of [362, 309, 22]-code), using
- 27 step Varšamov–Edel lengthening with (ri) = (1, 26 times 0) [i] based on linear OA(952, 334, F9, 21) (dual of [334, 282, 22]-code), using
- trace code [i] based on linear OA(8126, 167, F81, 21) (dual of [167, 141, 22]-code), using
- extended algebraic-geometric code AGe(F,145P) [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 167, using
- trace code [i] based on linear OA(8126, 167, F81, 21) (dual of [167, 141, 22]-code), using
- 27 step Varšamov–Edel lengthening with (ri) = (1, 26 times 0) [i] based on linear OA(952, 334, F9, 21) (dual of [334, 282, 22]-code), using
(53−21, 53, 51867)-Net in Base 9 — Upper bound on s
There is no (32, 53, 51868)-net in base 9, because
- 1 times m-reduction [i] would yield (32, 52, 51868)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 41 745846 016463 768539 522999 480181 988108 745496 074305 > 952 [i]