Best Known (84, 84+18, s)-Nets in Base 7
(84, 84+18, 13086)-Net over F7 — Constructive and digital
Digital (84, 102, 13086)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 13)-net over F7, using
- 3 times m-reduction [i] based on digital (1, 13, 13)-net over F7, using
- digital (74, 92, 13073)-net over F7, using
- net defined by OOA [i] based on linear OOA(792, 13073, F7, 18, 18) (dual of [(13073, 18), 235222, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(792, 117657, F7, 18) (dual of [117657, 117565, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(792, 117662, F7, 18) (dual of [117662, 117570, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- linear OA(791, 117649, F7, 18) (dual of [117649, 117558, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- 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]
- linear OA(71, 13, F7, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(792, 117662, F7, 18) (dual of [117662, 117570, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(792, 117657, F7, 18) (dual of [117657, 117565, 19]-code), using
- net defined by OOA [i] based on linear OOA(792, 13073, F7, 18, 18) (dual of [(13073, 18), 235222, 19]-NRT-code), using
- digital (1, 10, 13)-net over F7, using
(84, 84+18, 140737)-Net over F7 — Digital
Digital (84, 102, 140737)-net over F7, using
(84, 84+18, large)-Net in Base 7 — Upper bound on s
There is no (84, 102, large)-net in base 7, because
- 16 times m-reduction [i] would yield (84, 86, large)-net in base 7, but