Best Known (60−28, 60, s)-Nets in Base 81
(60−28, 60, 486)-Net over F81 — Constructive and digital
Digital (32, 60, 486)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (2, 16, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- digital (16, 44, 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 (2, 16, 116)-net over F81, using
(60−28, 60, 3289)-Net over F81 — Digital
Digital (32, 60, 3289)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8160, 3289, F81, 2, 28) (dual of [(3289, 2), 6518, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8160, 6578, F81, 28) (dual of [6578, 6518, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- linear OA(8155, 6561, F81, 28) (dual of [6561, 6506, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(8143, 6561, F81, 22) (dual of [6561, 6518, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(815, 17, F81, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,81)), using
- discarding factors / shortening the dual code based on linear OA(815, 81, F81, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), using
- Reed–Solomon code RS(76,81) [i]
- discarding factors / shortening the dual code based on linear OA(815, 81, F81, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- OOA 2-folding [i] based on linear OA(8160, 6578, F81, 28) (dual of [6578, 6518, 29]-code), using
(60−28, 60, large)-Net in Base 81 — Upper bound on s
There is no (32, 60, large)-net in base 81, because
- 26 times m-reduction [i] would yield (32, 34, large)-net in base 81, but