Best Known (48, 62, s)-Nets in Base 3
(48, 62, 400)-Net over F3 — Constructive and digital
Digital (48, 62, 400)-net over F3, using
- 32 times duplication [i] based on digital (46, 60, 400)-net over F3, using
- trace code for nets [i] based on digital (1, 15, 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
- trace code for nets [i] based on digital (1, 15, 100)-net over F81, using
(48, 62, 694)-Net over F3 — Digital
Digital (48, 62, 694)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(362, 694, F3, 14) (dual of [694, 632, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(362, 737, F3, 14) (dual of [737, 675, 15]-code), using
- (u, u+v)-construction [i] based on
- linear OA(37, 8, F3, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,3)), using
- dual of repetition code with length 8 [i]
- linear OA(355, 729, F3, 14) (dual of [729, 674, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(37, 8, F3, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,3)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(362, 737, F3, 14) (dual of [737, 675, 15]-code), using
(48, 62, 28426)-Net in Base 3 — Upper bound on s
There is no (48, 62, 28427)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 381585 287308 181039 899675 577763 > 362 [i]