MinT - Best Known (16, 77, s)-Nets in Base 16

Best Known (16, 77, s)-Nets in Base 16

(16, 77, 65)-Net over F₁₆ — Constructive and digital

Digital (16, 77, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 77, 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]

(16, 77, 98)-Net over F₁₆ — Digital

Digital (16, 77, 98)-net over F₁₆, using

t-expansion [i] based on digital (15, 77, 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]

(16, 77, 885)-Net in Base 16 — Upper bound on s

There is no (16, 77, 886)-net in base 16, because

1 times m-reduction [i] would yield (16, 76, 886)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 33 220456 322384 136550 210610 522160 415940 332946 770903 405977 560786 508238 634837 566584 245506 726576 > 16⁷⁶ [i]