MinT - Best Known (115−99, 115, s)-Nets in Base 16

Best Known (115−99, 115, s)-Nets in Base 16

(115−99, 115, 65)-Net over F₁₆ — Constructive and digital

Digital (16, 115, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 115, 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]

(115−99, 115, 98)-Net over F₁₆ — Digital

Digital (16, 115, 98)-net over F₁₆, using

t-expansion [i] based on digital (15, 115, 98)-net over F₁₆, using
- net from sequence [i] based on digital (15, 97)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 15 and N(F) ≥ 98, using
    - a curve from the manYPoints database [i]

(115−99, 115, 779)-Net in Base 16 — Upper bound on s

There is no (16, 115, 780)-net in base 16, because

1 times m-reduction [i] would yield (16, 114, 780)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 191540 392548 038989 258400 739159 469085 701414 152801 189409 523831 249951 982316 416385 882386 047668 770247 647798 125573 498406 195047 730801 281195 444176 > 16¹¹⁴ [i]