Best Known (122−107, 122, s)-Nets in Base 3
(122−107, 122, 28)-Net over F3 — Constructive and digital
Digital (15, 122, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
(122−107, 122, 40)-Net in Base 3 — Upper bound on s
There is no (15, 122, 41)-net in base 3, because
- 5 times m-reduction [i] would yield (15, 117, 41)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3117, 41, S3, 3, 102), but
- the LP bound with quadratic polynomials shows that M ≥ 8008 897756 408761 320483 431092 011943 448679 786438 779805 548281 / 103 > 3117 [i]
- extracting embedded OOA [i] would yield OOA(3117, 41, S3, 3, 102), but