Best Known (44, 44+26, s)-Nets in Base 9
(44, 44+26, 344)-Net over F9 — Constructive and digital
Digital (44, 70, 344)-net over F9, using
- 4 times m-reduction [i] based on digital (44, 74, 344)-net over F9, using
- trace code for nets [i] based on digital (7, 37, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 37, 172)-net over F81, using
(44, 44+26, 666)-Net over F9 — Digital
Digital (44, 70, 666)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(970, 666, F9, 26) (dual of [666, 596, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(970, 728, F9, 26) (dual of [728, 658, 27]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(970, 728, F9, 26) (dual of [728, 658, 27]-code), using
(44, 44+26, 97389)-Net in Base 9 — Upper bound on s
There is no (44, 70, 97390)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 6 266402 312050 013130 044720 020331 377634 900524 457774 330788 235159 082033 > 970 [i]