Best Known (97−21, 97, s)-Nets in Base 3
(97−21, 97, 464)-Net over F3 — Constructive and digital
Digital (76, 97, 464)-net over F3, using
- 31 times duplication [i] based on digital (75, 96, 464)-net over F3, using
- t-expansion [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
- t-expansion [i] based on digital (74, 96, 464)-net over F3, using
(97−21, 97, 1003)-Net over F3 — Digital
Digital (76, 97, 1003)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(397, 1003, F3, 21) (dual of [1003, 906, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(397, 1092, F3, 21) (dual of [1092, 995, 22]-code), using
(97−21, 97, 86151)-Net in Base 3 — Upper bound on s
There is no (76, 97, 86152)-net in base 3, because
- 1 times m-reduction [i] would yield (76, 96, 86152)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 6363 109724 648574 155755 655367 619885 034792 994609 > 396 [i]