MinT - Best Known (6, 67, s)-Nets in Base 16

Best Known (6, 67, s)-Nets in Base 16

(6, 67, 65)-Net over F₁₆ — Constructive and digital

Digital (6, 67, 65)-net over F₁₆, using

net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
  - the Hermitian function field over F₁₆ [i]

(6, 67, 257)-Net in Base 16 — Upper bound on s

There is no (6, 67, 258)-net in base 16, because

1 times m-reduction [i] would yield (6, 66, 258)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(16⁶⁶, 258, S₁₆, 60), but
  - the linear programming bound shows that MÂ â‰¥ 1 831068 329807 427886 693930 243021 843563 706420 919135 055008 442822 474518 284634 946184 791199 617279 638968 444720 313679 042286 103266 590720 / 61227 472926 450174 211522 981063 856899 560129 492773 > 16⁶⁶ [i]