Best Known (80, 102, s)-Nets in Base 3
(80, 102, 464)-Net over F3 — Constructive and digital
Digital (80, 102, 464)-net over F3, using
- 2 times m-reduction [i] based on digital (80, 104, 464)-net over F3, using
- trace code for nets [i] based on digital (2, 26, 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, 26, 116)-net over F81, using
(80, 102, 1100)-Net over F3 — Digital
Digital (80, 102, 1100)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3102, 1100, F3, 2, 22) (dual of [(1100, 2), 2098, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3102, 2200, F3, 22) (dual of [2200, 2098, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(399, 2187, F3, 22) (dual of [2187, 2088, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(385, 2187, F3, 19) (dual of [2187, 2102, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- OOA 2-folding [i] based on linear OA(3102, 2200, F3, 22) (dual of [2200, 2098, 23]-code), using
(80, 102, 65182)-Net in Base 3 — Upper bound on s
There is no (80, 102, 65183)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 4 638968 815539 106798 286489 684643 555600 163577 827947 > 3102 [i]