Best Known (74, 74+14, s)-Nets in Base 16
(74, 74+14, 2396766)-Net over F16 — Constructive and digital
Digital (74, 88, 2396766)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 24)-net over F16, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- digital (66, 80, 2396742)-net over F16, using
- trace code for nets [i] based on digital (26, 40, 1198371)-net over F256, using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- trace code for nets [i] based on digital (26, 40, 1198371)-net over F256, using
- digital (1, 8, 24)-net over F16, using
(74, 74+14, large)-Net over F16 — Digital
Digital (74, 88, large)-net over F16, using
- 2 times m-reduction [i] based on digital (74, 90, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(1690, large, F16, 16) (dual of [large, large−90, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(1690, large, F16, 16) (dual of [large, large−90, 17]-code), using
(74, 74+14, large)-Net in Base 16 — Upper bound on s
There is no (74, 88, large)-net in base 16, because
- 12 times m-reduction [i] would yield (74, 76, large)-net in base 16, but