Best Known (110, 110+34, s)-Nets in Base 3
(110, 110+34, 464)-Net over F3 — Constructive and digital
Digital (110, 144, 464)-net over F3, using
- trace code for nets [i] based on digital (2, 36, 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
(110, 110+34, 822)-Net over F3 — Digital
Digital (110, 144, 822)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3144, 822, F3, 34) (dual of [822, 678, 35]-code), using
- 79 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 0, 1, 0, 0, 1, 4 times 0, 1, 7 times 0, 1, 9 times 0, 1, 11 times 0, 1, 15 times 0, 1, 18 times 0) [i] based on linear OA(3130, 729, F3, 34) (dual of [729, 599, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- 79 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 0, 1, 0, 0, 1, 4 times 0, 1, 7 times 0, 1, 9 times 0, 1, 11 times 0, 1, 15 times 0, 1, 18 times 0) [i] based on linear OA(3130, 729, F3, 34) (dual of [729, 599, 35]-code), using
(110, 110+34, 39466)-Net in Base 3 — Upper bound on s
There is no (110, 144, 39467)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 507 582700 664628 843193 907656 317378 632210 885552 087520 143590 388510 649015 > 3144 [i]