Best Known (138−26, 138, s)-Nets in Base 5
(138−26, 138, 1219)-Net over F5 — Constructive and digital
Digital (112, 138, 1219)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (4, 17, 18)-net over F5, using
- net from sequence [i] based on digital (4, 17)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 4 and N(F) ≥ 18, using
- net from sequence [i] based on digital (4, 17)-sequence over F5, using
- digital (95, 121, 1201)-net over F5, using
- net defined by OOA [i] based on linear OOA(5121, 1201, F5, 26, 26) (dual of [(1201, 26), 31105, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(5121, 15613, F5, 26) (dual of [15613, 15492, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(5121, 15625, F5, 26) (dual of [15625, 15504, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(5121, 15625, F5, 26) (dual of [15625, 15504, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(5121, 15613, F5, 26) (dual of [15613, 15492, 27]-code), using
- net defined by OOA [i] based on linear OOA(5121, 1201, F5, 26, 26) (dual of [(1201, 26), 31105, 27]-NRT-code), using
- digital (4, 17, 18)-net over F5, using
(138−26, 138, 18373)-Net over F5 — Digital
Digital (112, 138, 18373)-net over F5, using
(138−26, 138, large)-Net in Base 5 — Upper bound on s
There is no (112, 138, large)-net in base 5, because
- 24 times m-reduction [i] would yield (112, 114, large)-net in base 5, but