Best Known (107−14, 107, s)-Nets in Base 7
(107−14, 107, 1647086)-Net over F7 — Constructive and digital
Digital (93, 107, 1647086)-net over F7, using
- 71 times duplication [i] based on digital (92, 106, 1647086)-net over F7, using
- trace code for nets [i] based on digital (39, 53, 823543)-net over F49, using
- net defined by OOA [i] based on linear OOA(4953, 823543, F49, 14, 14) (dual of [(823543, 14), 11529549, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(4953, 5764801, F49, 14) (dual of [5764801, 5764748, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- OA 7-folding and stacking [i] based on linear OA(4953, 5764801, F49, 14) (dual of [5764801, 5764748, 15]-code), using
- net defined by OOA [i] based on linear OOA(4953, 823543, F49, 14, 14) (dual of [(823543, 14), 11529549, 15]-NRT-code), using
- trace code for nets [i] based on digital (39, 53, 823543)-net over F49, using
(107−14, 107, large)-Net over F7 — Digital
Digital (93, 107, large)-net over F7, using
- 71 times duplication [i] based on digital (92, 106, large)-net over F7, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(7106, large, F7, 14) (dual of [large, large−106, 15]-code), using
- trace code [i] based on linear OA(4953, 5764801, F49, 14) (dual of [5764801, 5764748, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- trace code [i] based on linear OA(4953, 5764801, F49, 14) (dual of [5764801, 5764748, 15]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(7106, large, F7, 14) (dual of [large, large−106, 15]-code), using
(107−14, 107, large)-Net in Base 7 — Upper bound on s
There is no (93, 107, large)-net in base 7, because
- 12 times m-reduction [i] would yield (93, 95, large)-net in base 7, but