Best Known (91−25, 91, s)-Nets in Base 3
(91−25, 91, 204)-Net over F3 — Constructive and digital
Digital (66, 91, 204)-net over F3, using
- 31 times duplication [i] based on digital (65, 90, 204)-net over F3, using
- trace code for nets [i] based on digital (5, 30, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- trace code for nets [i] based on digital (5, 30, 68)-net over F27, using
(91−25, 91, 328)-Net over F3 — Digital
Digital (66, 91, 328)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(391, 328, F3, 25) (dual of [328, 237, 26]-code), using
- 74 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 8 times 0, 1, 10 times 0, 1, 10 times 0, 1, 12 times 0, 1, 12 times 0) [i] based on linear OA(381, 244, F3, 25) (dual of [244, 163, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 244 | 310−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 74 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 8 times 0, 1, 10 times 0, 1, 10 times 0, 1, 12 times 0, 1, 12 times 0) [i] based on linear OA(381, 244, F3, 25) (dual of [244, 163, 26]-code), using
(91−25, 91, 10005)-Net in Base 3 — Upper bound on s
There is no (66, 91, 10006)-net in base 3, because
- 1 times m-reduction [i] would yield (66, 90, 10006)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 8 732373 815358 034657 410550 863942 868329 454169 > 390 [i]