Best Known (93, 93+77, s)-Nets in Base 2
(93, 93+77, 53)-Net over F2 — Constructive and digital
Digital (93, 170, 53)-net over F2, using
- t-expansion [i] based on digital (90, 170, 53)-net over F2, using
- net from sequence [i] based on digital (90, 52)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 4 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (90, 52)-sequence over F2, using
(93, 93+77, 61)-Net over F2 — Digital
Digital (93, 170, 61)-net over F2, using
(93, 93+77, 275)-Net in Base 2 — Upper bound on s
There is no (93, 170, 276)-net in base 2, because
- 1 times m-reduction [i] would yield (93, 169, 276)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 806 605109 860369 819453 077184 905018 486688 906063 807776 > 2169 [i]