Best Known (84−74, 84, s)-Nets in Base 4
(84−74, 84, 27)-Net over F4 — Constructive and digital
Digital (10, 84, 27)-net over F4, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 10 and N(F) ≥ 27, using
(84−74, 84, 42)-Net in Base 4 — Upper bound on s
There is no (10, 84, 43)-net in base 4, because
- 3 times m-reduction [i] would yield (10, 81, 43)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(481, 43, S4, 2, 71), but
- the LP bound with quadratic polynomials shows that M ≥ 20 461022 922632 640854 851587 658027 962275 183055 601664 / 3 > 481 [i]
- extracting embedded OOA [i] would yield OOA(481, 43, S4, 2, 71), but