Best Known (118, 134, s)-Nets in Base 5
(118, 134, 1048595)-Net over F5 — Constructive and digital
Digital (118, 134, 1048595)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (5, 13, 20)-net over F5, using
- net from sequence [i] based on digital (5, 19)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 5 and N(F) ≥ 20, using
- net from sequence [i] based on digital (5, 19)-sequence over F5, using
- digital (105, 121, 1048575)-net over F5, using
- net defined by OOA [i] based on linear OOA(5121, 1048575, F5, 16, 16) (dual of [(1048575, 16), 16777079, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(5121, 8388600, F5, 16) (dual of [8388600, 8388479, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(5121, large, F5, 16) (dual of [large, large−121, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(5121, large, F5, 16) (dual of [large, large−121, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(5121, 8388600, F5, 16) (dual of [8388600, 8388479, 17]-code), using
- net defined by OOA [i] based on linear OOA(5121, 1048575, F5, 16, 16) (dual of [(1048575, 16), 16777079, 17]-NRT-code), using
- digital (5, 13, 20)-net over F5, using
(118, 134, 6601037)-Net over F5 — Digital
Digital (118, 134, 6601037)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5134, 6601037, F5, 16) (dual of [6601037, 6600903, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(5134, large, F5, 16) (dual of [large, large−134, 17]-code), using
- 13 times code embedding in larger space [i] based on linear OA(5121, large, F5, 16) (dual of [large, large−121, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 13 times code embedding in larger space [i] based on linear OA(5121, large, F5, 16) (dual of [large, large−121, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(5134, large, F5, 16) (dual of [large, large−134, 17]-code), using
(118, 134, large)-Net in Base 5 — Upper bound on s
There is no (118, 134, large)-net in base 5, because
- 14 times m-reduction [i] would yield (118, 120, large)-net in base 5, but