Best Known (36, 61, s)-Nets in Base 9
(36, 61, 320)-Net over F9 — Constructive and digital
Digital (36, 61, 320)-net over F9, using
- 1 times m-reduction [i] based on digital (36, 62, 320)-net over F9, using
- trace code for nets [i] based on digital (5, 31, 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, 31, 160)-net over F81, using
(36, 61, 345)-Net over F9 — Digital
Digital (36, 61, 345)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(961, 345, F9, 25) (dual of [345, 284, 26]-code), using
- 10 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0) [i] based on linear OA(960, 334, F9, 25) (dual of [334, 274, 26]-code), using
- trace code [i] based on linear OA(8130, 167, F81, 25) (dual of [167, 137, 26]-code), using
- extended algebraic-geometric code AGe(F,141P) [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 167, using
- trace code [i] based on linear OA(8130, 167, F81, 25) (dual of [167, 137, 26]-code), using
- 10 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0) [i] based on linear OA(960, 334, F9, 25) (dual of [334, 274, 26]-code), using
(36, 61, 39030)-Net in Base 9 — Upper bound on s
There is no (36, 61, 39031)-net in base 9, because
- 1 times m-reduction [i] would yield (36, 60, 39031)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 1797 188142 308877 920100 870830 919289 560543 638479 273592 692385 > 960 [i]