Best Known (35−10, 35, s)-Nets in Base 3
(35−10, 35, 114)-Net over F3 — Constructive and digital
Digital (25, 35, 114)-net over F3, using
- 1 times m-reduction [i] based on digital (25, 36, 114)-net over F3, using
- trace code for nets [i] based on digital (1, 12, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- trace code for nets [i] based on digital (1, 12, 38)-net over F27, using
(35−10, 35, 194)-Net over F3 — Digital
Digital (25, 35, 194)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(335, 194, F3, 10) (dual of [194, 159, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(335, 242, F3, 10) (dual of [242, 207, 11]-code), using
- the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(335, 242, F3, 10) (dual of [242, 207, 11]-code), using
(35−10, 35, 2844)-Net in Base 3 — Upper bound on s
There is no (25, 35, 2845)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 50096 774786 371659 > 335 [i]