Best Known (60−13, 60, s)-Nets in Base 3
(60−13, 60, 464)-Net over F3 — Constructive and digital
Digital (47, 60, 464)-net over F3, using
- trace code for nets [i] based on digital (2, 15, 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
(60−13, 60, 1100)-Net over F3 — Digital
Digital (47, 60, 1100)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(360, 1100, F3, 2, 13) (dual of [(1100, 2), 2140, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(360, 2200, F3, 13) (dual of [2200, 2140, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(357, 2187, F3, 13) (dual of [2187, 2130, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(343, 2187, F3, 10) (dual of [2187, 2144, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- OOA 2-folding [i] based on linear OA(360, 2200, F3, 13) (dual of [2200, 2140, 14]-code), using
(60−13, 60, 73595)-Net in Base 3 — Upper bound on s
There is no (47, 60, 73596)-net in base 3, because
- 1 times m-reduction [i] would yield (47, 59, 73596)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 14130 823229 347372 982566 821033 > 359 [i]