Best Known (102, 102+23, s)-Nets in Base 5
(102, 102+23, 1440)-Net over F5 — Constructive and digital
Digital (102, 125, 1440)-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 (86, 109, 1420)-net over F5, using
- net defined by OOA [i] based on linear OOA(5109, 1420, F5, 23, 23) (dual of [(1420, 23), 32551, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(5109, 15621, F5, 23) (dual of [15621, 15512, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(5109, 15625, F5, 23) (dual of [15625, 15516, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(5109, 15625, F5, 23) (dual of [15625, 15516, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(5109, 15621, F5, 23) (dual of [15621, 15512, 24]-code), using
- net defined by OOA [i] based on linear OOA(5109, 1420, F5, 23, 23) (dual of [(1420, 23), 32551, 24]-NRT-code), using
- digital (5, 16, 20)-net over F5, using
(102, 102+23, 21205)-Net over F5 — Digital
Digital (102, 125, 21205)-net over F5, using
(102, 102+23, large)-Net in Base 5 — Upper bound on s
There is no (102, 125, large)-net in base 5, because
- 21 times m-reduction [i] would yield (102, 104, large)-net in base 5, but