Best Known (99, 99+98, s)-Nets in Base 2
(99, 99+98, 54)-Net over F2 — Constructive and digital
Digital (99, 197, 54)-net over F2, using
- t-expansion [i] based on digital (95, 197, 54)-net over F2, using
- net from sequence [i] based on digital (95, 53)-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 5 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 (95, 53)-sequence over F2, using
(99, 99+98, 65)-Net over F2 — Digital
Digital (99, 197, 65)-net over F2, using
- t-expansion [i] based on digital (95, 197, 65)-net over F2, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 95 and N(F) ≥ 65, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
(99, 99+98, 213)-Net over F2 — Upper bound on s (digital)
There is no digital (99, 197, 214)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2197, 214, F2, 98) (dual of [214, 17, 99]-code), but
- residual code [i] would yield OA(299, 115, S2, 49), but
- 1 times truncation [i] would yield OA(298, 114, S2, 48), but
- the linear programming bound shows that M ≥ 141449 524575 866749 536608 130468 675584 / 431375 > 298 [i]
- 1 times truncation [i] would yield OA(298, 114, S2, 48), but
- residual code [i] would yield OA(299, 115, S2, 49), but
(99, 99+98, 244)-Net in Base 2 — Upper bound on s
There is no (99, 197, 245)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 231299 670306 675673 975156 310271 796327 608106 253105 200143 281442 > 2197 [i]