Best Known (15, 15+10, s)-Nets in Base 81
(15, 15+10, 1412)-Net over F81 — Constructive and digital
Digital (15, 25, 1412)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- digital (9, 19, 1312)-net over F81, using
- net defined by OOA [i] based on linear OOA(8119, 1312, F81, 10, 10) (dual of [(1312, 10), 13101, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(8119, 6560, F81, 10) (dual of [6560, 6541, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(8119, 6561, F81, 10) (dual of [6561, 6542, 11]-code), using
- an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(8119, 6561, F81, 10) (dual of [6561, 6542, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(8119, 6560, F81, 10) (dual of [6560, 6541, 11]-code), using
- net defined by OOA [i] based on linear OOA(8119, 1312, F81, 10, 10) (dual of [(1312, 10), 13101, 11]-NRT-code), using
- digital (1, 6, 100)-net over F81, using
(15, 15+10, 10380)-Net over F81 — Digital
Digital (15, 25, 10380)-net over F81, using
(15, 15+10, large)-Net in Base 81 — Upper bound on s
There is no (15, 25, large)-net in base 81, because
- 8 times m-reduction [i] would yield (15, 17, large)-net in base 81, but