Best Known (97−22, 97, s)-Nets in Base 3
(97−22, 97, 464)-Net over F3 — Constructive and digital
Digital (75, 97, 464)-net over F3, using
- 31 times duplication [i] based on digital (74, 96, 464)-net over F3, using
- trace code for nets [i] based on digital (2, 24, 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, 24, 116)-net over F81, using
(97−22, 97, 786)-Net over F3 — Digital
Digital (75, 97, 786)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(397, 786, F3, 22) (dual of [786, 689, 23]-code), using
- 45 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 9 times 0, 1, 13 times 0) [i] based on linear OA(385, 729, F3, 22) (dual of [729, 644, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 45 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 9 times 0, 1, 13 times 0) [i] based on linear OA(385, 729, F3, 22) (dual of [729, 644, 23]-code), using
(97−22, 97, 39555)-Net in Base 3 — Upper bound on s
There is no (75, 97, 39556)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 19088 775773 021797 635382 057775 125321 920109 079793 > 397 [i]