Best Known (78, 94, s)-Nets in Base 5
(78, 94, 9775)-Net over F5 — Constructive and digital
Digital (78, 94, 9775)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 10)-net over F5, using
- net from sequence [i] based on digital (1, 9)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 1 and N(F) ≥ 10, using
- net from sequence [i] based on digital (1, 9)-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 (1, 9, 10)-net over F5, using
(78, 94, 66450)-Net over F5 — Digital
Digital (78, 94, 66450)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(594, 66450, F5, 16) (dual of [66450, 66356, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(594, 78136, F5, 16) (dual of [78136, 78042, 17]-code), using
- (u, u+v)-construction [i] based on
- linear OA(59, 11, F5, 8) (dual of [11, 2, 9]-code), using
- 1 times truncation [i] based on linear OA(510, 12, F5, 9) (dual of [12, 2, 10]-code), using
- repeating each code word 2 times [i] based on linear OA(54, 6, F5, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,5)), using
- extended Reed–Solomon code RSe(2,5) [i]
- Simplex code S(2,5) [i]
- repeating each code word 2 times [i] based on linear OA(54, 6, F5, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,5)), using
- 1 times truncation [i] based on linear OA(510, 12, F5, 9) (dual of [12, 2, 10]-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(59, 11, F5, 8) (dual of [11, 2, 9]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(594, 78136, F5, 16) (dual of [78136, 78042, 17]-code), using
(78, 94, large)-Net in Base 5 — Upper bound on s
There is no (78, 94, large)-net in base 5, because
- 14 times m-reduction [i] would yield (78, 80, large)-net in base 5, but