Best Known (135−30, 135, s)-Nets in Base 3
(135−30, 135, 464)-Net over F3 — Constructive and digital
Digital (105, 135, 464)-net over F3, using
- t-expansion [i] based on digital (104, 135, 464)-net over F3, using
- 1 times m-reduction [i] based on digital (104, 136, 464)-net over F3, using
- trace code for nets [i] based on digital (2, 34, 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
- trace code for nets [i] based on digital (2, 34, 116)-net over F81, using
- 1 times m-reduction [i] based on digital (104, 136, 464)-net over F3, using
(135−30, 135, 986)-Net over F3 — Digital
Digital (105, 135, 986)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3135, 986, F3, 30) (dual of [986, 851, 31]-code), using
- 240 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 1, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 7 times 0, 1, 10 times 0, 1, 13 times 0, 1, 17 times 0, 1, 21 times 0, 1, 24 times 0, 1, 28 times 0, 1, 30 times 0, 1, 32 times 0, 1, 34 times 0) [i] based on linear OA(3117, 728, F3, 30) (dual of [728, 611, 31]-code), using
- the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 240 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 1, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 7 times 0, 1, 10 times 0, 1, 13 times 0, 1, 17 times 0, 1, 21 times 0, 1, 24 times 0, 1, 28 times 0, 1, 30 times 0, 1, 32 times 0, 1, 34 times 0) [i] based on linear OA(3117, 728, F3, 30) (dual of [728, 611, 31]-code), using
(135−30, 135, 63201)-Net in Base 3 — Upper bound on s
There is no (105, 135, 63202)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 25787 360415 455584 326690 231325 135298 026893 360138 782346 749952 511257 > 3135 [i]