Best Known (39−16, 39, s)-Nets in Base 9
(39−16, 39, 232)-Net over F9 — Constructive and digital
Digital (23, 39, 232)-net over F9, using
- 3 times m-reduction [i] based on digital (23, 42, 232)-net over F9, using
- trace code for nets [i] based on digital (2, 21, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- trace code for nets [i] based on digital (2, 21, 116)-net over F81, using
(39−16, 39, 276)-Net over F9 — Digital
Digital (23, 39, 276)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(939, 276, F9, 16) (dual of [276, 237, 17]-code), using
- 3 step Varšamov–Edel lengthening with (ri) = (1, 0, 0) [i] based on linear OA(938, 272, F9, 16) (dual of [272, 234, 17]-code), using
- trace code [i] based on linear OA(8119, 136, F81, 16) (dual of [136, 117, 17]-code), using
- extended algebraic-geometric code AGe(F,119P) [i] based on function field F/F81 with g(F) = 3 and N(F) ≥ 136, using
- trace code [i] based on linear OA(8119, 136, F81, 16) (dual of [136, 117, 17]-code), using
- 3 step Varšamov–Edel lengthening with (ri) = (1, 0, 0) [i] based on linear OA(938, 272, F9, 16) (dual of [272, 234, 17]-code), using
(39−16, 39, 21107)-Net in Base 9 — Upper bound on s
There is no (23, 39, 21108)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 16 425425 243689 893370 484007 386162 825985 > 939 [i]