Best Known (21, 35, s)-Nets in Base 5
(21, 35, 104)-Net over F5 — Constructive and digital
Digital (21, 35, 104)-net over F5, using
- 1 times m-reduction [i] based on digital (21, 36, 104)-net over F5, using
- trace code for nets [i] based on digital (3, 18, 52)-net over F25, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F25, using
- trace code for nets [i] based on digital (3, 18, 52)-net over F25, using
(21, 35, 120)-Net over F5 — Digital
Digital (21, 35, 120)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(535, 120, F5, 14) (dual of [120, 85, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(535, 132, F5, 14) (dual of [132, 97, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(534, 125, F5, 14) (dual of [125, 91, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(528, 125, F5, 12) (dual of [125, 97, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(51, 7, F5, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(535, 132, F5, 14) (dual of [132, 97, 15]-code), using
(21, 35, 2635)-Net in Base 5 — Upper bound on s
There is no (21, 35, 2636)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 2 911231 166811 994975 715505 > 535 [i]