Best Known (117, 117+27, s)-Nets in Base 5
(117, 117+27, 1220)-Net over F5 — Constructive and digital
Digital (117, 144, 1220)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (4, 17, 18)-net over F5, using
- net from sequence [i] based on digital (4, 17)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 4 and N(F) ≥ 18, using
- net from sequence [i] based on digital (4, 17)-sequence over F5, using
- digital (100, 127, 1202)-net over F5, using
- net defined by OOA [i] based on linear OOA(5127, 1202, F5, 27, 27) (dual of [(1202, 27), 32327, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(5127, 15627, F5, 27) (dual of [15627, 15500, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(5127, 15631, F5, 27) (dual of [15631, 15504, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(5127, 15625, F5, 27) (dual of [15625, 15498, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(5121, 15625, F5, 26) (dual of [15625, 15504, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(50, 6, F5, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(5127, 15631, F5, 27) (dual of [15631, 15504, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(5127, 15627, F5, 27) (dual of [15627, 15500, 28]-code), using
- net defined by OOA [i] based on linear OOA(5127, 1202, F5, 27, 27) (dual of [(1202, 27), 32327, 28]-NRT-code), using
- digital (4, 17, 18)-net over F5, using
(117, 117+27, 19622)-Net over F5 — Digital
Digital (117, 144, 19622)-net over F5, using
(117, 117+27, large)-Net in Base 5 — Upper bound on s
There is no (117, 144, large)-net in base 5, because
- 25 times m-reduction [i] would yield (117, 119, large)-net in base 5, but