Best Known (16, 27, s)-Nets in Base 81
(16, 27, 1412)-Net over F81 — Constructive and digital
Digital (16, 27, 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 (10, 21, 1312)-net over F81, using
- net defined by OOA [i] based on linear OOA(8121, 1312, F81, 11, 11) (dual of [(1312, 11), 14411, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(8121, 6561, F81, 11) (dual of [6561, 6540, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(8121, 6561, F81, 11) (dual of [6561, 6540, 12]-code), using
- net defined by OOA [i] based on linear OOA(8121, 1312, F81, 11, 11) (dual of [(1312, 11), 14411, 12]-NRT-code), using
- digital (1, 6, 100)-net over F81, using
(16, 27, 8055)-Net over F81 — Digital
Digital (16, 27, 8055)-net over F81, using
(16, 27, large)-Net in Base 81 — Upper bound on s
There is no (16, 27, large)-net in base 81, because
- 9 times m-reduction [i] would yield (16, 18, large)-net in base 81, but