Best Known (44, 44+10, s)-Nets in Base 5
(44, 44+10, 3135)-Net over F5 — Constructive and digital
Digital (44, 54, 3135)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 10)-net over F5, using
- net from sequence [i] based on digital (1, 9)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 1 and N(F) ≥ 10, using
- net from sequence [i] based on digital (1, 9)-sequence over F5, using
- digital (38, 48, 3125)-net over F5, using
- net defined by OOA [i] based on linear OOA(548, 3125, F5, 10, 10) (dual of [(3125, 10), 31202, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(548, 15625, F5, 10) (dual of [15625, 15577, 11]-code), using
- 1 times truncation [i] based on linear OA(549, 15626, F5, 11) (dual of [15626, 15577, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(549, 15626, F5, 11) (dual of [15626, 15577, 12]-code), using
- OA 5-folding and stacking [i] based on linear OA(548, 15625, F5, 10) (dual of [15625, 15577, 11]-code), using
- net defined by OOA [i] based on linear OOA(548, 3125, F5, 10, 10) (dual of [(3125, 10), 31202, 11]-NRT-code), using
- digital (1, 6, 10)-net over F5, using
(44, 44+10, 16204)-Net over F5 — Digital
Digital (44, 54, 16204)-net over F5, using
(44, 44+10, large)-Net in Base 5 — Upper bound on s
There is no (44, 54, large)-net in base 5, because
- 8 times m-reduction [i] would yield (44, 46, large)-net in base 5, but