Best Known (154−36, 154, s)-Nets in Base 3
(154−36, 154, 464)-Net over F3 — Constructive and digital
Digital (118, 154, 464)-net over F3, using
- 32 times duplication [i] based on digital (116, 152, 464)-net over F3, using
- trace code for nets [i] based on digital (2, 38, 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, 38, 116)-net over F81, using
(154−36, 154, 892)-Net over F3 — Digital
Digital (118, 154, 892)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3154, 892, F3, 36) (dual of [892, 738, 37]-code), using
- 151 step Varšamov–Edel lengthening with (ri) = (2, 1, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 13 times 0, 1, 17 times 0, 1, 20 times 0, 1, 22 times 0, 1, 24 times 0, 1, 25 times 0) [i] based on linear OA(3141, 728, F3, 36) (dual of [728, 587, 37]-code), using
- the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- 151 step Varšamov–Edel lengthening with (ri) = (2, 1, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 13 times 0, 1, 17 times 0, 1, 20 times 0, 1, 22 times 0, 1, 24 times 0, 1, 25 times 0) [i] based on linear OA(3141, 728, F3, 36) (dual of [728, 587, 37]-code), using
(154−36, 154, 45600)-Net in Base 3 — Upper bound on s
There is no (118, 154, 45601)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 29 973429 547031 845560 230384 015084 657555 721207 885032 316523 675889 336486 584969 > 3154 [i]