Best Known (121, 121+23, s)-Nets in Base 5
(121, 121+23, 7123)-Net over F5 — Constructive and digital
Digital (121, 144, 7123)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (6, 17, 21)-net over F5, using
- net from sequence [i] based on digital (6, 20)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 6 and N(F) ≥ 21, using
- net from sequence [i] based on digital (6, 20)-sequence over F5, using
- digital (104, 127, 7102)-net over F5, using
- net defined by OOA [i] based on linear OOA(5127, 7102, F5, 23, 23) (dual of [(7102, 23), 163219, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(5127, 78123, F5, 23) (dual of [78123, 77996, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(5127, 78125, F5, 23) (dual of [78125, 77998, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(5127, 78125, F5, 23) (dual of [78125, 77998, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(5127, 78123, F5, 23) (dual of [78123, 77996, 24]-code), using
- net defined by OOA [i] based on linear OOA(5127, 7102, F5, 23, 23) (dual of [(7102, 23), 163219, 24]-NRT-code), using
- digital (6, 17, 21)-net over F5, using
(121, 121+23, 85099)-Net over F5 — Digital
Digital (121, 144, 85099)-net over F5, using
(121, 121+23, large)-Net in Base 5 — Upper bound on s
There is no (121, 144, large)-net in base 5, because
- 21 times m-reduction [i] would yield (121, 123, large)-net in base 5, but