Best Known (58−23, 58, s)-Nets in Base 9
(58−23, 58, 320)-Net over F9 — Constructive and digital
Digital (35, 58, 320)-net over F9, using
- 2 times m-reduction [i] based on digital (35, 60, 320)-net over F9, using
- trace code for nets [i] based on digital (5, 30, 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, 30, 160)-net over F81, using
(58−23, 58, 383)-Net over F9 — Digital
Digital (35, 58, 383)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(958, 383, F9, 23) (dual of [383, 325, 24]-code), using
- 47 step Varšamov–Edel lengthening with (ri) = (1, 15 times 0, 1, 30 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
- 47 step Varšamov–Edel lengthening with (ri) = (1, 15 times 0, 1, 30 times 0) [i] based on linear OA(956, 334, F9, 23) (dual of [334, 278, 24]-code), using
(58−23, 58, 54023)-Net in Base 9 — Upper bound on s
There is no (35, 58, 54024)-net in base 9, because
- 1 times m-reduction [i] would yield (35, 57, 54024)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 2 465198 630006 423366 750486 978031 985070 615346 000719 120833 > 957 [i]