Best Known (92, 92+16, s)-Nets in Base 5
(92, 92+16, 48844)-Net over F5 — Constructive and digital
Digital (92, 108, 48844)-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 (81, 97, 48828)-net over F5, using
- net defined by OOA [i] based on linear OOA(597, 48828, F5, 16, 16) (dual of [(48828, 16), 781151, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(597, 390624, F5, 16) (dual of [390624, 390527, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(597, 390625, F5, 16) (dual of [390625, 390528, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(597, 390625, F5, 16) (dual of [390625, 390528, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(597, 390624, F5, 16) (dual of [390624, 390527, 17]-code), using
- net defined by OOA [i] based on linear OOA(597, 48828, F5, 16, 16) (dual of [(48828, 16), 781151, 17]-NRT-code), using
- digital (3, 11, 16)-net over F5, using
(92, 92+16, 332287)-Net over F5 — Digital
Digital (92, 108, 332287)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5108, 332287, F5, 16) (dual of [332287, 332179, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(5108, 390637, F5, 16) (dual of [390637, 390529, 17]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(55, 6, F5, 5) (dual of [6, 1, 6]-code or 6-arc in PG(4,5)), using
- dual of repetition code with length 6 [i]
- linear OA(56, 6, F5, 6) (dual of [6, 0, 7]-code or 6-arc in PG(5,5)), using
- linear OA(597, 390625, F5, 16) (dual of [390625, 390528, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(55, 6, F5, 5) (dual of [6, 1, 6]-code or 6-arc in PG(4,5)), using
- (u, u−v, u+v+w)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(5108, 390637, F5, 16) (dual of [390637, 390529, 17]-code), using
(92, 92+16, large)-Net in Base 5 — Upper bound on s
There is no (92, 108, large)-net in base 5, because
- 14 times m-reduction [i] would yield (92, 94, large)-net in base 5, but