Best Known (102, 102+18, s)-Nets in Base 3
(102, 102+18, 6561)-Net over F3 — Constructive and digital
Digital (102, 120, 6561)-net over F3, using
- net defined by OOA [i] based on linear OOA(3120, 6561, F3, 18, 18) (dual of [(6561, 18), 117978, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(3120, 59049, F3, 18) (dual of [59049, 58929, 19]-code), using
- 1 times truncation [i] based on linear OA(3121, 59050, F3, 19) (dual of [59050, 58929, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(3121, 59050, F3, 19) (dual of [59050, 58929, 20]-code), using
- OA 9-folding and stacking [i] based on linear OA(3120, 59049, F3, 18) (dual of [59049, 58929, 19]-code), using
(102, 102+18, 19683)-Net over F3 — Digital
Digital (102, 120, 19683)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3120, 19683, F3, 3, 18) (dual of [(19683, 3), 58929, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3120, 59049, F3, 18) (dual of [59049, 58929, 19]-code), using
- 1 times truncation [i] based on linear OA(3121, 59050, F3, 19) (dual of [59050, 58929, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(3121, 59050, F3, 19) (dual of [59050, 58929, 20]-code), using
- OOA 3-folding [i] based on linear OA(3120, 59049, F3, 18) (dual of [59049, 58929, 19]-code), using
(102, 102+18, 4768012)-Net in Base 3 — Upper bound on s
There is no (102, 120, 4768013)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1797 011157 593443 920202 801838 159455 292857 057112 033334 146043 > 3120 [i]