Best Known (90−16, 90, s)-Nets in Base 7
(90−16, 90, 14720)-Net over F7 — Constructive and digital
Digital (74, 90, 14720)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (3, 11, 14)-net over F7, using
- 3 times m-reduction [i] based on digital (3, 14, 14)-net over F7, using
- digital (63, 79, 14706)-net over F7, using
- net defined by OOA [i] based on linear OOA(779, 14706, F7, 16, 16) (dual of [(14706, 16), 235217, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(779, 117648, F7, 16) (dual of [117648, 117569, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(779, 117649, F7, 16) (dual of [117649, 117570, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(779, 117649, F7, 16) (dual of [117649, 117570, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(779, 117648, F7, 16) (dual of [117648, 117569, 17]-code), using
- net defined by OOA [i] based on linear OOA(779, 14706, F7, 16, 16) (dual of [(14706, 16), 235217, 17]-NRT-code), using
- digital (3, 11, 14)-net over F7, using
(90−16, 90, 125959)-Net over F7 — Digital
Digital (74, 90, 125959)-net over F7, using
(90−16, 90, large)-Net in Base 7 — Upper bound on s
There is no (74, 90, large)-net in base 7, because
- 14 times m-reduction [i] would yield (74, 76, large)-net in base 7, but