Best Known (63−26, 63, s)-Nets in Base 9
(63−26, 63, 320)-Net over F9 — Constructive and digital
Digital (37, 63, 320)-net over F9, using
- 1 times m-reduction [i] based on digital (37, 64, 320)-net over F9, using
- trace code for nets [i] based on digital (5, 32, 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, 32, 160)-net over F81, using
(63−26, 63, 343)-Net over F9 — Digital
Digital (37, 63, 343)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(963, 343, F9, 26) (dual of [343, 280, 27]-code), using
- 8 step Varšamov–Edel lengthening with (ri) = (1, 7 times 0) [i] based on linear OA(962, 334, F9, 26) (dual of [334, 272, 27]-code), using
- trace code [i] based on linear OA(8131, 167, F81, 26) (dual of [167, 136, 27]-code), using
- extended algebraic-geometric code AGe(F,140P) [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 167, using
- trace code [i] based on linear OA(8131, 167, F81, 26) (dual of [167, 136, 27]-code), using
- 8 step Varšamov–Edel lengthening with (ri) = (1, 7 times 0) [i] based on linear OA(962, 334, F9, 26) (dual of [334, 272, 27]-code), using
(63−26, 63, 29827)-Net in Base 9 — Upper bound on s
There is no (37, 63, 29828)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 1 310527 744405 891893 496479 464692 855328 656273 765047 086423 455905 > 963 [i]