Best Known (93−25, 93, s)-Nets in Base 9
(93−25, 93, 740)-Net over F9 — Constructive and digital
Digital (68, 93, 740)-net over F9, using
- 11 times m-reduction [i] based on digital (68, 104, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 52, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 52, 370)-net over F81, using
(93−25, 93, 6582)-Net over F9 — Digital
Digital (68, 93, 6582)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(993, 6582, F9, 25) (dual of [6582, 6489, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(989, 6562, F9, 25) (dual of [6562, 6473, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(973, 6562, F9, 21) (dual of [6562, 6489, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 98−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(94, 20, F9, 3) (dual of [20, 16, 4]-code or 20-cap in PG(3,9)), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
(93−25, 93, large)-Net in Base 9 — Upper bound on s
There is no (68, 93, large)-net in base 9, because
- 23 times m-reduction [i] would yield (68, 70, large)-net in base 9, but