Best Known (32, 32+29, s)-Nets in Base 3
(32, 32+29, 38)-Net over F3 — Constructive and digital
Digital (32, 61, 38)-net over F3, using
- net from sequence [i] based on digital (32, 37)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 32 and N(F) ≥ 38, using
(32, 32+29, 45)-Net over F3 — Digital
Digital (32, 61, 45)-net over F3, using
(32, 32+29, 321)-Net in Base 3 — Upper bound on s
There is no (32, 61, 322)-net in base 3, because
- 1 times m-reduction [i] would yield (32, 60, 322)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 42624 795428 925801 991761 918477 > 360 [i]