MinT - Best Known (8, 8+36, s)-Nets in Base 16

Best Known (8, 8+36, s)-Nets in Base 16

(8, 8+36, 65)-Net over F₁₆ — Constructive and digital

Digital (8, 44, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 44, 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]

(8, 8+36, 432)-Net in Base 16 — Upper bound on s

There is no (8, 44, 433)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 98244 416849 794320 652374 828074 987033 617418 821195 504336 > 16⁴⁴ [i]