Best Known (22, 37, s)-Nets in Base 9
(22, 37, 232)-Net over F9 — Constructive and digital
Digital (22, 37, 232)-net over F9, using
- 3 times m-reduction [i] based on digital (22, 40, 232)-net over F9, using
- trace code for nets [i] based on digital (2, 20, 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, 20, 116)-net over F81, using
(22, 37, 279)-Net over F9 — Digital
Digital (22, 37, 279)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(937, 279, F9, 15) (dual of [279, 242, 16]-code), using
- 6 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0) [i] based on linear OA(936, 272, F9, 15) (dual of [272, 236, 16]-code), using
- trace code [i] based on linear OA(8118, 136, F81, 15) (dual of [136, 118, 16]-code), using
- extended algebraic-geometric code AGe(F,120P) [i] based on function field F/F81 with g(F) = 3 and N(F) ≥ 136, using
- trace code [i] based on linear OA(8118, 136, F81, 15) (dual of [136, 118, 16]-code), using
- 6 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0) [i] based on linear OA(936, 272, F9, 15) (dual of [272, 236, 16]-code), using
(22, 37, 34143)-Net in Base 9 — Upper bound on s
There is no (22, 37, 34144)-net in base 9, because
- 1 times m-reduction [i] would yield (22, 36, 34144)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 22529 167325 110668 081971 382280 849665 > 936 [i]