Best Known (43−36, 43, s)-Nets in Base 128
(43−36, 43, 216)-Net over F128 — Constructive and digital
Digital (7, 43, 216)-net over F128, using
- t-expansion [i] based on digital (5, 43, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
(43−36, 43, 258)-Net in Base 128 — Constructive
(7, 43, 258)-net in base 128, using
- 5 times m-reduction [i] based on (7, 48, 258)-net in base 128, using
- base change [i] based on digital (1, 42, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 42, 258)-net over F256, using
(43−36, 43, 262)-Net over F128 — Digital
Digital (7, 43, 262)-net over F128, using
- net from sequence [i] based on digital (7, 261)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 7 and N(F) ≥ 262, using
(43−36, 43, 289)-Net in Base 128
(7, 43, 289)-net in base 128, using
- 5 times m-reduction [i] based on (7, 48, 289)-net in base 128, using
- base change [i] based on digital (1, 42, 289)-net over F256, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- base change [i] based on digital (1, 42, 289)-net over F256, using
(43−36, 43, 6421)-Net in Base 128 — Upper bound on s
There is no (7, 43, 6422)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 4 080382 215579 366053 263255 244745 864506 222109 166308 330658 208735 657826 288698 010928 873561 708306 > 12843 [i]