Best Known (46, 60, s)-Nets in Base 81
(46, 60, 1198453)-Net over F81 — Constructive and digital
Digital (46, 60, 1198453)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- digital (39, 53, 1198371)-net over F81, using
- net defined by OOA [i] based on linear OOA(8153, 1198371, F81, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(8153, 8388597, F81, 14) (dual of [8388597, 8388544, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(8153, large, F81, 14) (dual of [large, large−53, 15]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(8153, large, F81, 14) (dual of [large, large−53, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(8153, 8388597, F81, 14) (dual of [8388597, 8388544, 15]-code), using
- net defined by OOA [i] based on linear OOA(8153, 1198371, F81, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
- digital (0, 7, 82)-net over F81, using
(46, 60, large)-Net over F81 — Digital
Digital (46, 60, large)-net over F81, using
- t-expansion [i] based on digital (45, 60, large)-net over F81, using
- 1 times m-reduction [i] based on digital (45, 61, large)-net over F81, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8161, large, F81, 16) (dual of [large, large−61, 17]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8161, large, F81, 16) (dual of [large, large−61, 17]-code), using
- 1 times m-reduction [i] based on digital (45, 61, large)-net over F81, using
(46, 60, large)-Net in Base 81 — Upper bound on s
There is no (46, 60, large)-net in base 81, because
- 12 times m-reduction [i] would yield (46, 48, large)-net in base 81, but