Best Known (153, 153+18, s)-Nets in Base 4
(153, 153+18, 932084)-Net over F4 — Constructive and digital
Digital (153, 171, 932084)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 14, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- 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 (5, 14, 17)-net over F4, using
(153, 153+18, 5653325)-Net over F4 — Digital
Digital (153, 171, 5653325)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4171, 5653325, F4, 18) (dual of [5653325, 5653154, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(4171, large, F4, 18) (dual of [large, large−171, 19]-code), using
- 14 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]
- 14 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(4171, large, F4, 18) (dual of [large, large−171, 19]-code), using
(153, 153+18, large)-Net in Base 4 — Upper bound on s
There is no (153, 171, large)-net in base 4, because
- 16 times m-reduction [i] would yield (153, 155, large)-net in base 4, but