Best Known (38, 63, s)-Nets in Base 9
(38, 63, 320)-Net over F9 — Constructive and digital
Digital (38, 63, 320)-net over F9, using
- 3 times m-reduction [i] based on digital (38, 66, 320)-net over F9, using
- trace code for nets [i] based on digital (5, 33, 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, 33, 160)-net over F81, using
(38, 63, 406)-Net over F9 — Digital
Digital (38, 63, 406)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(963, 406, F9, 25) (dual of [406, 343, 26]-code), using
- 25 step Varšamov–Edel lengthening with (ri) = (1, 24 times 0) [i] based on linear OA(962, 380, F9, 25) (dual of [380, 318, 26]-code), using
- trace code [i] based on linear OA(8131, 190, F81, 25) (dual of [190, 159, 26]-code), using
- extended algebraic-geometric code AGe(F,164P) [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- trace code [i] based on linear OA(8131, 190, F81, 25) (dual of [190, 159, 26]-code), using
- 25 step Varšamov–Edel lengthening with (ri) = (1, 24 times 0) [i] based on linear OA(962, 380, F9, 25) (dual of [380, 318, 26]-code), using
(38, 63, 56295)-Net in Base 9 — Upper bound on s
There is no (38, 63, 56296)-net in base 9, because
- 1 times m-reduction [i] would yield (38, 62, 56296)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 145586 560939 567937 805009 519156 711374 399609 316335 039816 556801 > 962 [i]