Best Known (48, 48+29, s)-Nets in Base 81
(48, 48+29, 740)-Net over F81 — Constructive and digital
Digital (48, 77, 740)-net over F81, using
- t-expansion [i] based on digital (47, 77, 740)-net over F81, using
- 2 times m-reduction [i] based on digital (47, 79, 740)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (15, 31, 820)-net over F81, using
- net defined by OOA [i] based on linear OOA(8131, 820, F81, 16, 16) (dual of [(820, 16), 13089, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(8131, 6560, F81, 16) (dual of [6560, 6529, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(8131, 6561, F81, 16) (dual of [6561, 6530, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(8131, 6561, F81, 16) (dual of [6561, 6530, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(8131, 6560, F81, 16) (dual of [6560, 6529, 17]-code), using
- net defined by OOA [i] based on linear OOA(8131, 820, F81, 16, 16) (dual of [(820, 16), 13089, 17]-NRT-code), using
- digital (16, 48, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- digital (15, 31, 820)-net over F81, using
- (u, u+v)-construction [i] based on
- 2 times m-reduction [i] based on digital (47, 79, 740)-net over F81, using
(48, 48+29, 25032)-Net over F81 — Digital
Digital (48, 77, 25032)-net over F81, using
(48, 48+29, large)-Net in Base 81 — Upper bound on s
There is no (48, 77, large)-net in base 81, because
- 27 times m-reduction [i] would yield (48, 50, large)-net in base 81, but