Best Known (47−18, 47, s)-Nets in Base 9
(47−18, 47, 320)-Net over F9 — Constructive and digital
Digital (29, 47, 320)-net over F9, using
- 1 times m-reduction [i] based on digital (29, 48, 320)-net over F9, using
- trace code for nets [i] based on digital (5, 24, 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, 24, 160)-net over F81, using
(47−18, 47, 399)-Net over F9 — Digital
Digital (29, 47, 399)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(947, 399, F9, 18) (dual of [399, 352, 19]-code), using
- 121 step Varšamov–Edel lengthening with (ri) = (1, 8 times 0, 1, 26 times 0, 1, 38 times 0, 1, 45 times 0) [i] based on linear OA(943, 274, F9, 18) (dual of [274, 231, 19]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(942, 272, F9, 18) (dual of [272, 230, 19]-code), using
- trace code [i] based on linear OA(8121, 136, F81, 18) (dual of [136, 115, 19]-code), using
- extended algebraic-geometric code AGe(F,117P) [i] based on function field F/F81 with g(F) = 3 and N(F) ≥ 136, using
- trace code [i] based on linear OA(8121, 136, F81, 18) (dual of [136, 115, 19]-code), using
- linear OA(942, 273, F9, 17) (dual of [273, 231, 18]-code), using Gilbert–Varšamov bound and bm = 942 > Vbs−1(k−1) = 7761 874144 032175 513657 339926 096418 973313 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(942, 272, F9, 18) (dual of [272, 230, 19]-code), using
- construction X with Varšamov bound [i] based on
- 121 step Varšamov–Edel lengthening with (ri) = (1, 8 times 0, 1, 26 times 0, 1, 38 times 0, 1, 45 times 0) [i] based on linear OA(943, 274, F9, 18) (dual of [274, 231, 19]-code), using
(47−18, 47, 49875)-Net in Base 9 — Upper bound on s
There is no (29, 47, 49876)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 707 087232 247218 547698 266688 475127 519417 552289 > 947 [i]