Best Known (80−65, 80, s)-Nets in Base 64
(80−65, 80, 177)-Net over F64 — Constructive and digital
Digital (15, 80, 177)-net over F64, using
- t-expansion [i] based on digital (7, 80, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
(80−65, 80, 192)-Net in Base 64 — Constructive
(15, 80, 192)-net in base 64, using
- 4 times m-reduction [i] based on (15, 84, 192)-net in base 64, using
- base change [i] based on digital (3, 72, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 72, 192)-net over F128, using
(80−65, 80, 258)-Net over F64 — Digital
Digital (15, 80, 258)-net over F64, using
- net from sequence [i] based on digital (15, 257)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 15 and N(F) ≥ 258, using
(80−65, 80, 5825)-Net in Base 64 — Upper bound on s
There is no (15, 80, 5826)-net in base 64, because
- 1 times m-reduction [i] would yield (15, 79, 5826)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 48830 794636 829113 721733 076058 331768 924761 580283 791474 898004 049094 476541 422152 864942 597789 282595 597783 719047 800494 826492 743022 484611 074104 000402 > 6479 [i]