MinT - Best Known (6, 6+59, s)-Nets in Base 16

Best Known (6, 6+59, s)-Nets in Base 16

(6, 6+59, 65)-Net over F₁₆ — Constructive and digital

Digital (6, 65, 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, 6+59, 258)-Net in Base 16 — Upper bound on s

There is no (6, 65, 259)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁶⁵, 259, S₁₆, 59), but
- the linear programming bound shows that MÂ â‰¥ 56 276572 650645 541349 006166 971411 454658 492486 845808 946236 493211 500346 203572 796245 849632 672306 232020 495859 526278 030448 483343 794176 / 30 003791 214490 297290 429534 847599 708209 937909 006961 > 16⁶⁵ [i]