Best Known (57−23, 57, s)-Nets in Base 9
(57−23, 57, 320)-Net over F9 — Constructive and digital
Digital (34, 57, 320)-net over F9, using
- 1 times m-reduction [i] based on digital (34, 58, 320)-net over F9, using
- trace code for nets [i] based on digital (5, 29, 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, 29, 160)-net over F81, using
(57−23, 57, 351)-Net over F9 — Digital
Digital (34, 57, 351)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(957, 351, F9, 23) (dual of [351, 294, 24]-code), using
- 16 step Varšamov–Edel lengthening with (ri) = (1, 15 times 0) [i] based on linear OA(956, 334, F9, 23) (dual of [334, 278, 24]-code), using
- trace code [i] based on linear OA(8128, 167, F81, 23) (dual of [167, 139, 24]-code), using
- extended algebraic-geometric code AGe(F,143P) [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 167, using
- trace code [i] based on linear OA(8128, 167, F81, 23) (dual of [167, 139, 24]-code), using
- 16 step Varšamov–Edel lengthening with (ri) = (1, 15 times 0) [i] based on linear OA(956, 334, F9, 23) (dual of [334, 278, 24]-code), using
(57−23, 57, 44240)-Net in Base 9 — Upper bound on s
There is no (34, 57, 44241)-net in base 9, because
- 1 times m-reduction [i] would yield (34, 56, 44241)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 273902 962289 193355 465876 598266 909067 914609 562551 423385 > 956 [i]