Best Known (80, 80+16, s)-Nets in Base 5
(80, 80+16, 9781)-Net over F5 — Constructive and digital
Digital (80, 96, 9781)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (3, 11, 16)-net over F5, using
- net from sequence [i] based on digital (3, 15)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 3 and N(F) ≥ 16, using
- net from sequence [i] based on digital (3, 15)-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 (3, 11, 16)-net over F5, using
(80, 80+16, 78170)-Net over F5 — Digital
Digital (80, 96, 78170)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(596, 78170, F5, 16) (dual of [78170, 78074, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(8) [i] 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]
- linear OA(550, 78125, F5, 9) (dual of [78125, 78075, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(511, 45, F5, 6) (dual of [45, 34, 7]-code), using
- construction X applied to Ce(15) ⊂ Ce(8) [i] based on
(80, 80+16, large)-Net in Base 5 — Upper bound on s
There is no (80, 96, large)-net in base 5, because
- 14 times m-reduction [i] would yield (80, 82, large)-net in base 5, but