Best Known (82, 82+19, s)-Nets in Base 5
(82, 82+19, 1746)-Net over F5 — Constructive and digital
Digital (82, 101, 1746)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 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
- a shift-net [i]
- net from sequence [i] based on digital (1, 9)-sequence over F5, using
- digital (72, 91, 1736)-net over F5, using
- net defined by OOA [i] based on linear OOA(591, 1736, F5, 19, 19) (dual of [(1736, 19), 32893, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OOA 9-folding and stacking with additional row [i] based on linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using
- net defined by OOA [i] based on linear OOA(591, 1736, F5, 19, 19) (dual of [(1736, 19), 32893, 20]-NRT-code), using
- digital (1, 10, 10)-net over F5, using
(82, 82+19, 15787)-Net over F5 — Digital
Digital (82, 101, 15787)-net over F5, using
(82, 82+19, large)-Net in Base 5 — Upper bound on s
There is no (82, 101, large)-net in base 5, because
- 17 times m-reduction [i] would yield (82, 84, large)-net in base 5, but