Best Known (121, 149, s)-Nets in Base 5
(121, 149, 1128)-Net over F5 — Constructive and digital
Digital (121, 149, 1128)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (2, 16, 12)-net over F5, using
- net from sequence [i] based on digital (2, 11)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 2 and N(F) ≥ 12, using
- net from sequence [i] based on digital (2, 11)-sequence over F5, using
- digital (105, 133, 1116)-net over F5, using
- net defined by OOA [i] based on linear OOA(5133, 1116, F5, 28, 28) (dual of [(1116, 28), 31115, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(5133, 15624, F5, 28) (dual of [15624, 15491, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(5133, 15625, F5, 28) (dual of [15625, 15492, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(5133, 15625, F5, 28) (dual of [15625, 15492, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(5133, 15624, F5, 28) (dual of [15624, 15491, 29]-code), using
- net defined by OOA [i] based on linear OOA(5133, 1116, F5, 28, 28) (dual of [(1116, 28), 31115, 29]-NRT-code), using
- digital (2, 16, 12)-net over F5, using
(121, 149, 19675)-Net over F5 — Digital
Digital (121, 149, 19675)-net over F5, using
(121, 149, large)-Net in Base 5 — Upper bound on s
There is no (121, 149, large)-net in base 5, because
- 26 times m-reduction [i] would yield (121, 123, large)-net in base 5, but