Best Known (135−34, 135, s)-Nets in Base 3
(135−34, 135, 288)-Net over F3 — Constructive and digital
Digital (101, 135, 288)-net over F3, using
- trace code for nets [i] based on digital (11, 45, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(135−34, 135, 609)-Net over F3 — Digital
Digital (101, 135, 609)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3135, 609, F3, 34) (dual of [609, 474, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3135, 728, F3, 34) (dual of [728, 593, 35]-code), using
- the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- discarding factors / shortening the dual code based on linear OA(3135, 728, F3, 34) (dual of [728, 593, 35]-code), using
(135−34, 135, 22054)-Net in Base 3 — Upper bound on s
There is no (101, 135, 22055)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 25797 707895 637882 563015 822138 081913 288547 715508 071201 544775 825967 > 3135 [i]