Best Known (117−22, 117, s)-Nets in Base 5
(117−22, 117, 1437)-Net over F5 — Constructive and digital
Digital (95, 117, 1437)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (3, 14, 16)-net over F5, using
- net from sequence [i] based on digital (3, 15)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 3 and N(F) ≥ 16, using
- net from sequence [i] based on digital (3, 15)-sequence over F5, using
- digital (81, 103, 1421)-net over F5, using
- net defined by OOA [i] based on linear OOA(5103, 1421, F5, 22, 22) (dual of [(1421, 22), 31159, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(5103, 15631, F5, 22) (dual of [15631, 15528, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(5103, 15625, F5, 22) (dual of [15625, 15522, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(597, 15625, F5, 21) (dual of [15625, 15528, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(50, 6, F5, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- OA 11-folding and stacking [i] based on linear OA(5103, 15631, F5, 22) (dual of [15631, 15528, 23]-code), using
- net defined by OOA [i] based on linear OOA(5103, 1421, F5, 22, 22) (dual of [(1421, 22), 31159, 23]-NRT-code), using
- digital (3, 14, 16)-net over F5, using
(117−22, 117, 17020)-Net over F5 — Digital
Digital (95, 117, 17020)-net over F5, using
(117−22, 117, large)-Net in Base 5 — Upper bound on s
There is no (95, 117, large)-net in base 5, because
- 20 times m-reduction [i] would yield (95, 97, large)-net in base 5, but