Best Known (70, 70+17, s)-Nets in Base 5
(70, 70+17, 1959)-Net over F5 — Constructive and digital
Digital (70, 87, 1959)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 6)-net over F5, using
- net from sequence [i] based on digital (0, 5)-sequence over F5, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 0 and N(F) ≥ 6, using
- the rational function field F5(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 5)-sequence over F5, using
- digital (62, 79, 1953)-net over F5, using
- net defined by OOA [i] based on linear OOA(579, 1953, F5, 17, 17) (dual of [(1953, 17), 33122, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(579, 15625, F5, 17) (dual of [15625, 15546, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(579, 15625, F5, 17) (dual of [15625, 15546, 18]-code), using
- net defined by OOA [i] based on linear OOA(579, 1953, F5, 17, 17) (dual of [(1953, 17), 33122, 18]-NRT-code), using
- digital (0, 8, 6)-net over F5, using
(70, 70+17, 15658)-Net over F5 — Digital
Digital (70, 87, 15658)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(587, 15658, F5, 17) (dual of [15658, 15571, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- linear OA(579, 15625, F5, 17) (dual of [15625, 15546, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(549, 15625, F5, 11) (dual of [15625, 15576, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(58, 33, F5, 5) (dual of [33, 25, 6]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
(70, 70+17, large)-Net in Base 5 — Upper bound on s
There is no (70, 87, large)-net in base 5, because
- 15 times m-reduction [i] would yield (70, 72, large)-net in base 5, but