Best Known (91, 91+79, s)-Nets in Base 4
(91, 91+79, 130)-Net over F4 — Constructive and digital
Digital (91, 170, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 85, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(91, 91+79, 157)-Net over F4 — Digital
Digital (91, 170, 157)-net over F4, using
(91, 91+79, 2053)-Net in Base 4 — Upper bound on s
There is no (91, 170, 2054)-net in base 4, because
- 1 times m-reduction [i] would yield (91, 169, 2054)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 562193 136313 338227 739459 484829 587736 824511 459704 769843 959605 880776 954551 442403 757722 514018 676094 167040 > 4169 [i]