Best Known (105, 105+24, s)-Nets in Base 3
(105, 105+24, 688)-Net over F3 — Constructive and digital
Digital (105, 129, 688)-net over F3, using
- 31 times duplication [i] based on digital (104, 128, 688)-net over F3, using
- t-expansion [i] based on digital (103, 128, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 32, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 32, 172)-net over F81, using
- t-expansion [i] based on digital (103, 128, 688)-net over F3, using
(105, 105+24, 3284)-Net over F3 — Digital
Digital (105, 129, 3284)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3129, 3284, F3, 2, 24) (dual of [(3284, 2), 6439, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3129, 6568, F3, 24) (dual of [6568, 6439, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3129, 6569, F3, 24) (dual of [6569, 6440, 25]-code), using
- 1 times truncation [i] based on linear OA(3130, 6570, F3, 25) (dual of [6570, 6440, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(3129, 6561, F3, 25) (dual of [6561, 6432, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3121, 6561, F3, 23) (dual of [6561, 6440, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(31, 9, F3, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- 1 times truncation [i] based on linear OA(3130, 6570, F3, 25) (dual of [6570, 6440, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3129, 6569, F3, 24) (dual of [6569, 6440, 25]-code), using
- OOA 2-folding [i] based on linear OA(3129, 6568, F3, 24) (dual of [6568, 6439, 25]-code), using
(105, 105+24, 355935)-Net in Base 3 — Upper bound on s
There is no (105, 129, 355936)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 35 371570 729312 355295 181848 038600 595988 626670 264591 962937 276673 > 3129 [i]