MinT - Best Known (84−79, 84, s)-Nets in Base 16

Best Known (84−79, 84, s)-Nets in Base 16

(84−79, 84, 49)-Net over F₁₆ — Constructive and digital

Digital (5, 84, 49)-net over F₁₆, using

net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
  - a function field by SÃ©mirat [i]

(84−79, 84, 115)-Net in Base 16 — Upper bound on s

There is no (5, 84, 116)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁸⁴, 116, S₁₆, 79), but
- the linear programming bound shows that MÂ â‰¥ 12 141833 554231 696812 666102 132976 420200 205022 010054 554589 786966 947621 011980 316220 647524 531590 133676 191898 099618 152448 / 84 213697 591023 > 16⁸⁴ [i]