Best Known (79, 79+16, s)-Nets in Base 5
(79, 79+16, 9777)-Net over F5 — Constructive and digital
Digital (79, 95, 9777)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (2, 10, 12)-net over F5, using
- net from sequence [i] based on digital (2, 11)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 2 and N(F) ≥ 12, using
- net from sequence [i] based on digital (2, 11)-sequence over F5, using
- digital (69, 85, 9765)-net over F5, using
- net defined by OOA [i] based on linear OOA(585, 9765, F5, 16, 16) (dual of [(9765, 16), 156155, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(585, 78120, F5, 16) (dual of [78120, 78035, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(585, 78120, F5, 16) (dual of [78120, 78035, 17]-code), using
- net defined by OOA [i] based on linear OOA(585, 9765, F5, 16, 16) (dual of [(9765, 16), 156155, 17]-NRT-code), using
- digital (2, 10, 12)-net over F5, using
(79, 79+16, 74546)-Net over F5 — Digital
Digital (79, 95, 74546)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(595, 74546, F5, 16) (dual of [74546, 74451, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(595, 78138, F5, 16) (dual of [78138, 78043, 17]-code), using
- (u, u+v)-construction [i] based on
- linear OA(510, 13, F5, 8) (dual of [13, 3, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(510, 15, F5, 8) (dual of [15, 5, 9]-code), using
- linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(510, 13, F5, 8) (dual of [13, 3, 9]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(595, 78138, F5, 16) (dual of [78138, 78043, 17]-code), using
(79, 79+16, large)-Net in Base 5 — Upper bound on s
There is no (79, 95, large)-net in base 5, because
- 14 times m-reduction [i] would yield (79, 81, large)-net in base 5, but