Best Known (104, 128, s)-Nets in Base 5
(104, 128, 1312)-Net over F5 — Constructive and digital
Digital (104, 128, 1312)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 10)-net over F5, using
- net from sequence [i] based on digital (1, 9)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 1 and N(F) ≥ 10, using
- net from sequence [i] based on digital (1, 9)-sequence over F5, using
- digital (91, 115, 1302)-net over F5, using
- net defined by OOA [i] based on linear OOA(5115, 1302, F5, 24, 24) (dual of [(1302, 24), 31133, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(5115, 15624, F5, 24) (dual of [15624, 15509, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(5115, 15625, F5, 24) (dual of [15625, 15510, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(5115, 15625, F5, 24) (dual of [15625, 15510, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(5115, 15624, F5, 24) (dual of [15624, 15509, 25]-code), using
- net defined by OOA [i] based on linear OOA(5115, 1302, F5, 24, 24) (dual of [(1302, 24), 31133, 25]-NRT-code), using
- digital (1, 13, 10)-net over F5, using
(104, 128, 18306)-Net over F5 — Digital
Digital (104, 128, 18306)-net over F5, using
(104, 128, large)-Net in Base 5 — Upper bound on s
There is no (104, 128, large)-net in base 5, because
- 22 times m-reduction [i] would yield (104, 106, large)-net in base 5, but