Best Known (114, 136, s)-Nets in Base 5
(114, 136, 7122)-Net over F5 — Constructive and digital
Digital (114, 136, 7122)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (5, 16, 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 (98, 120, 7102)-net over F5, using
- net defined by OOA [i] based on linear OOA(5120, 7102, F5, 22, 22) (dual of [(7102, 22), 156124, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(5120, 78122, F5, 22) (dual of [78122, 78002, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(5120, 78125, F5, 22) (dual of [78125, 78005, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(5120, 78125, F5, 22) (dual of [78125, 78005, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(5120, 78122, F5, 22) (dual of [78122, 78002, 23]-code), using
- net defined by OOA [i] based on linear OOA(5120, 7102, F5, 22, 22) (dual of [(7102, 22), 156124, 23]-NRT-code), using
- digital (5, 16, 20)-net over F5, using
(114, 136, 78187)-Net over F5 — Digital
Digital (114, 136, 78187)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5136, 78187, F5, 22) (dual of [78187, 78051, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(12) [i] based on
- linear OA(5120, 78125, F5, 22) (dual of [78125, 78005, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(571, 78125, F5, 13) (dual of [78125, 78054, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(516, 62, F5, 8) (dual of [62, 46, 9]-code), using
- a “LX†code from Brouwer’s database [i]
- construction X applied to Ce(21) ⊂ Ce(12) [i] based on
(114, 136, large)-Net in Base 5 — Upper bound on s
There is no (114, 136, large)-net in base 5, because
- 20 times m-reduction [i] would yield (114, 116, large)-net in base 5, but