Best Known (174−18, 174, s)-Nets in Base 4
(174−18, 174, 932091)-Net over F4 — Constructive and digital
Digital (156, 174, 932091)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (8, 17, 24)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 10)-net over F4, using
- digital (3, 12, 14)-net over F4, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- (u, u+v)-construction [i] based on
- digital (139, 157, 932067)-net over F4, using
- net defined by OOA [i] based on linear OOA(4157, 932067, F4, 18, 18) (dual of [(932067, 18), 16777049, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(4157, large, F4, 18) (dual of [large, large−157, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(4157, large, F4, 18) (dual of [large, large−157, 19]-code), using
- net defined by OOA [i] based on linear OOA(4157, 932067, F4, 18, 18) (dual of [(932067, 18), 16777049, 19]-NRT-code), using
- digital (8, 17, 24)-net over F4, using
(174−18, 174, 7331459)-Net over F4 — Digital
Digital (156, 174, 7331459)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4174, 7331459, F4, 18) (dual of [7331459, 7331285, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(4174, large, F4, 18) (dual of [large, large−174, 19]-code), using
- 17 times code embedding in larger space [i] based on linear OA(4157, large, F4, 18) (dual of [large, large−157, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 17 times code embedding in larger space [i] based on linear OA(4157, large, F4, 18) (dual of [large, large−157, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(4174, large, F4, 18) (dual of [large, large−174, 19]-code), using
(174−18, 174, large)-Net in Base 4 — Upper bound on s
There is no (156, 174, large)-net in base 4, because
- 16 times m-reduction [i] would yield (156, 158, large)-net in base 4, but